So Artosis did a Starcraft Brood War unit tier list.
https://www.youtube.com/watch?v=NWfZiQEHgj0I don't really agree with all of his placements, but it's a good jumping off point.
First, I want to discuss what the probe, drone, SCV, and overlord rankings actually mean, since obviously if you told someone they couldn't build these, they just wouldn't be able to do anything. Artosis makes some pretty good points with the probe and how a probe on the map is really dangerous:
1. Probe can gas steal
2. Probe can cannon rush
3. Probe is good at scouting and harassment due to regenerating shields
So like...when I ask a question like "can you win without probes?" it's going to imply "can you win without sending probes out on the map, without attacking with probes, or using probes for combat functions like blocking ramps?" And...you can, but you are certainly hurt in several ways--you'll struggle with early scouting, your early offense options are significantly diminished, you can't play greedy and then defend against cheese with probe micro.
One other thing I want to declare in advance--Artosis made declarations on unit power based on whether they are used in all matchups, and I agree with that BUT I'm going to put slightly less weight on mirror matchups. (Like...the defiler is almost never used in ZvZ, but should that lower its tier ranking? Probably not, right--it's still so impactful against the two other matchups. Meanwhile, the Battlecruiser is used almost entirely in TvT, which means deleting it from the game would not upset race balance).
Ok, so
S-tier, these are units that are way out of line at what they do, basically end up defining brood war. These are units that if you had access to all three races you'd be looking to build:
S: Zergling, Mutalisk, Defiler, High Templar, Siege Tank, Science Vessel
Zergling damage is just well above what would be expected. Worth noting that it was substantially reduced in starcraft 2. The zergling is a matchup defining unit built in large numbers in all three matchups.
Mutalisks are funny because their stats were actually buffed for starcraft 2, and they're not nearly as good there. The AI pathfinding is just so bad in brood war that flying units that don't get stuck bumping into each other are very hard to deal with. In addition, nearly all damage that hits air is explosive damage, which means mutalisks take half damage from it. And of the base flying units, mutalisks are the only ones that have a ground attack just as good as their air attack, making them a threat even to people building full ground armies.
Defiler spells just warp how you have to play against Zerg. A lot of armies just can't damage under Dark Swarm at all. And Plague outright shuts down a lot of strategies and units against zerg. Being able to get energy back fast with consume is also excellent.
High Templar...brood war storm is special. Compared to Starcraft 2 storm, it's like 50% more damage, and does its full damage in half the time, so even if you react quickly and move out of the storm, you still take tons of damage.
If Siege Tanks could hit air, I don't think there would be any army that could reliably beat mass siege tank. Not that they can't ever be broken with ground units, but in a ground war they are generally the most important unit.
Science Vessels are just completely matchup-defining in Terran vs Zerg. In a lategame TvZ, casters will tell you to not look at the supply count, not look at anything the zerg has, just look at the Science Vessel count, and this will be the most accurate measure of who is winning. They're also very powerful in TvP. Just being a detector is very useful against both Dark Templar and Arbiters. EMP removes all shields which is excellent damage, but also blanks out the energy on spellcasters like high templar and arbiters. Defense Matrix is also a highly useful spell in the right situation.
---
A-tier these are units that the race would really struggle to function without. If you couldn't use these units (in a combat role) for a day, the race would be in a lot of trouble in multiple matchups. If you had access to all races, you definitely would think about using some of these.
A: Vulture, Probe, Overlord, Dragoon, Zealot, Scourge
Vulture is honestly on the A/S borderline. What they do is pretty ridiculous for 75 minerals. Fastest unit in the game. Able to drop 3 mines, any one of which can one-shot more expensive units. Able to kill worker lines. Able to give lots of map vision with mines. But...they're non-essential against zerg, and in TvT they're more of an earlygame thing that drops off. I did just watch an FFA custom map where people had access to all races, and only one player made vultures, switching off of them later in the game once they had upgrades on zerglings.
Probe as discussed is the scariest worker, can cannon rush, is excellent at harassment, can build an assimilator in the opponent's base to gas steal. Is pretty essential for scouting since protoss really doesn't have a good alternative for an early scout. As well as all the normal things you expect out of workers like helping defend against rushes.
Overlords are excellent detection, so good at scouting that zerg often doesn't even bother with sending a scouting drone, good for dropping, as well as being basically free cause you're going to build them anyway for supply. I've straight up seen an overlord get mind controlled in a game that had become a 1v1, cause the protoss needed a dropship, and then later it was used as a detector. There might be an argument for S-tier here, but ehh...just because you build overlords doesn't mean you'll get drop upgrades or bring them with your army for detection.
Dragoon among all of the massable ranged units that can hit air like Hydralisks and Goliaths and Marines are just clearly the best. Why are they the best? Cause Marines have 40 HP, Hydralisks have 80 HP, Goliaths have 125 HP, and Psionic Storm deals 120 damage. But Dragoons have 180 HP (and they are also really fat, so even poorly controlled they don't bunch up as much against splash damage like storm and siege tanks).
Zealots get used in every matchup, they're a great mineral sink, they are basically zerglings with 4x the health, but then ultralisks are zealots with not even 4x the health, so you know.
Scourge get a lot of value in every matchup, and are just probably the best anti-air option in the game. The existence of scourge just changes how you have to play against zerg.
---
B-tier: These are units that are still kind-of game warping, or just really important to the functionality of their race.
B-tier: Lurker, Shuttle, Goliath, Dark Templar, Arbiter, Reaver, Dropship, SCV, Observer
Lurker: my first pass of this had these in A-tier because they are so central to Zerg lategame, but in the end I'm conceding Artosis this one, every other race has better ground AoE. Zerg needs some kind of ground AoE, so they cling to lurkers, and it is essential to them, but they're not siege tanks, and they're not high templar. Not even close.
Shuttle, Dropship: Yeah, so look, Shuttle is definitely a little better than Dropship, and my original list reflected this, but bottom line, neither Terran nor Protoss wants to give up shuttles or dropships in any matchup. Would you build either of these if you had access to all three races? Fuck no, you'd use overlords. If you had access to only Terran and Protoss would you ever build a Dropship? I mean, you might, if you teched to starport before stargate. Dropships are also faster than Shuttles before getting the shuttle upgrade (after which shuttle is faster). I think, while one of these is clearly a bit better, they are close enough to be same tier.
Golaith: You never really want to mass up on these, you just do so as a response to air units. They do have the best ground to air attack, of course (8 range, much more damage than their ground to ground attack). And are just all around pretty good units (even their ground attack is honestly fairly solid).
Dark Templar: If you told a protoss player they had to not build Dark Templar, they could...function. No one race requires going DT. But they are quite strong, including in subtle ways (if they kill something in one hit, like a worker, there's no notification, so even pro players don't necessarily notice). Usable in all three matchups. Reasonably important vs T.
Reaver: As I've mentioned before, I'm putting less weight on mirror matchups, and this does just break PvP. But in the other matchups...it's okay. You can make Reavers against Terran or Zerg, and they are quite effective. But it wouldn't be weird to play a match against Terran or Zerg without them.
SCV: These do three things above and beyond a regular worker that I think deserves a callout in this tier. One is scout. Marines are a terrible scouting option, and it's not great to wait until vulture. Another is repairing. They can repair tanks, and that's pretty good. Another is building turrets next to their tanks in the middle of the map. SCVs are worth bringing with a tank push against both Terran and Protoss, and I think that, along with all the other things that workers do like using them to defend rushes, is enough to justify them in this tier.
Observer: look, yes, observers are the worst detection, they move really slow, they have garbage vision range, I get it. But it's a little like the Lurker, yeah, your race is bad at this, what are you gonna do, not bother? LOL good luck with that.
---
C-tier: The race definitely doesn't want to lose these, but it might only hurt them in one matchup
Corsair, Marine, Medic, Archon, Hydra, Drone
Corsairs are only used in one matchup (against zerg) but of the games I've watched recently, corsairs get built basically every game against zerg. The only thing holding corsairs back is that they have no ground attack. Other than that, remember how I said mutas were good because they are light, and everything that hits air deals explosive damage? Corsairs are medium, so they also benefit from that (but not as much). Tons of health (180). Their singletarget damage against air is fine (about the same as a dragoon) but they have AoE splash. And they're tied for the fastest air unit. And they can moving shot. And their build time is fast (tied for fastest build time among protoss units). The only thing that holds them back is that air units suck so no one builds them, so they have nothing to shoot at. The moment they have air units to kill (against zerg) they are pretty great.
Marines and Medics are non-viable in two matchups cause they get murdered by splash damage at long range, but they are very core against zerg. Not completely core, you can go mech, but still most TvZ games are still Marine Medic.
Archons are units you'd only ever actually want against zerg, since they're solid against zerglings. But they are basically free after high templar so you'll use them incidentally in other matchups.
Hydralisks tend to end up being core against Protoss. Which is funny, for years against protoss you wouldn't see many of them, it's not like they're great units. But then corsairs were everywhere, and hydras are the only ground unit zerg has that can attack air units. And building air units to kill corsairs is suicide, because the Corsairs will win. Basically, because corsairs are meta, Zerg has to go hydra every time against protoss.
Drone really doesn't do anything special the way the other workers do. But you can attack with them if you get rushed. And defending rushes is still a sufficiently core enough part of the game that I don't think it makes sense to put Drone lower than C-tier.
---
D-tier: These units are used rarely or are used in one matchup but not every game
Firebat, Wraith, Carrier, Ultralisk
Firebat is used lategame as a way to fight against dark swarm, since they will do full damage underneath dark swarm (and also have pretty good AoE against zerglings).
Wraith is...something I basically don't see against protoss, occasionally see against zerg as a way of killing overlords or killing guardains, and is pretty good in Terran vs Terran to prevent the opponent from building only siege tanks, but I weigh mirror matches a little bit lower.
Carrier is built almost exclusively in Protoss vs Terran, and even then it's not that popular of a tech switch in the high level games I've watched recently. You need a lot of time, with a lot of your resources and army basically hidden (it's very bad if it gets scanned early allowing the Terran to switch into Goliaths).
Ultralisk is used almost exclusively in Zerg vs Terran these days. I do remember years ago seeing them against protoss, but I believe they are just a one race unit now. Compared to the Zealot they have 2.5x the health, with 1.8x the damage, for 4x the price. So the same way the zealot is less efficient but fatter than the zergling, the ultra is less efficient but fatter than the zealot. But unlike the zealot they cost gas too. But still, they have fast movement speed (with the upgrade faster than zealots), and if you upgrade their armour then subtraction defence means marines struggle to kill them. So they can be a lategame pick in this matchup sometimes.
---
E-tier: limited to relatively niche uses in usually one matchup
Guardian, Valkyrie, Queen, Dark Archon, Battlecruiser, Ghost
Guardians get used sometimes when a terran has countered the mutalisks, but might not have a good way of dealing with guardians, or when there's a really weird map with a bunch of open space. They tend not to be used against protoss unless all the corsairs get killed. They don't show up against zerg. Against Terran they tend to be a one-time "gotcha" surprise. I do wonder about moving these up to D-tier, since I do see them in pro games a decent amount, but I mean, they're definitely a step below carriers and ultralisks and firebats, so this is probably the place for them.
Valkyries are used...other than the mirror matchup where all the bad terran air units get made, get used sometimes as a response when Zerg goes unusually mutalisk heavy, and any other build would die to them (science vessels are not fast enough for the mass muta surprise kill you).
Queens are made sometimes when a lategame Terran goes very tank heavy, and then spawn broodling can be used to kill the tanks. This requires a ton of planning ahead, hiding the queens for a long time since Spawn Broodling costs 150 energy. There are also some niche uses to queens; ensnare completely negates the effects of stim on marines, which means there are some timing builds that use queens. There is some argument for these in D-tier, but...I just don't see them in pro matches as often as I see ultralisks, and see them more often used as a tank counter than a stim marine counter (and the 150 energy buildup thing where you need to hide them for that long is a fairly harsh limitation for that, plus it's more of a reactive response if the terran is going too tank heavy, can't just autopilot tech to queens).
Dark Archon is on the lower end of this group I think? If you can tech to them, they are very scary. Mind control can completely change the game. Maelstrom is excellent against zerg. But...I very rarely see anyone tech to them at all.
Battlecruisers are really only used in Terran vs Terran. Against Protoss they are too weak to arbiters. Against Zerg they will occasionally get used as harassment in ones or twoes. But mostly it's a lategame option against Terran (much like Carriers and Ultras are lategame anti-terran options). But I'm weighing mirror matches lower--if Battlecruisers stopped existing, it would do almost nothing to the balance of the game.
Ghosts are also a primarily Terran vs Terran thing. You build them, you nuke some tank lines. They do also have some fringe potential against carriers hitting them with lockdown.
---
F-tier In the end my F-tier ended up being the same as Artosis, I feel least confident about these units and the ones in E-tier, so I may just be trusting his judgment here.
Devourer, Scout, Broodling
Devourer: they can have some fringe uses as an anti-corsair or anti carrier unit. But not on their own, they apply a debuff but deal basically no damage themselves, and then rely on other units to clean up. They do pop up in pro games very occasionally, but man they are pretty underwhelming.
Scout: I think I've maybe seen these in a pro game once? They are fine air-to-air against one big target like a carrier, and they have a ground attack (even if their ground attack is terrible). But like...yeah, terrans don't build any anti-air early on against protoss, so sometimes they can be caught off-guard occasionally by a scout. But..still it's easy to make fun of the scout, cause they're basically a bad wraith. 4 range to Wraith's 5 range. No cloak. They move much slower (unless you get an upgrade, then they match the wraith's movement). They cost 60% more, but deal the same ground damage and 40% more air damage. Their one big win is having roughly double the health of a Wraith. But man, "bad wraith" is not a great selling point.
Broodling: Actually I will deviate from Artosis on this one point--Broodlings can cause siege tanks to deal splash damage to each other, so I don't think they belong in FF tier.
---
FF-tier Inested Terran
Infested Terran...searching for any pro games that actually use these, the two that I could find were literally on a map with a neutral command center in the middle of the map to be infested. (To be fair, they do seem like decent units against a protoss who's making zealots and high templar, but yeah, normally you could only even theoretically get these against terran, and you'd never be able to protect the building).