Go go Greil Mercenaries. I don't have a problem with Gatrie myself, since you get him back earlier and a bit more easily than Shinon, and he's a lot more useful. On the other hand, I don't care too much about Rolf, though I'll give him a yes if he makes it to the ranking topic.
Elincia is a definite yes, despite possible level discrepancies due to her late joining time.
Tanith and Marcia both have a bit of plot thrown in, though certainly not much. Guess I'll support Marcia to avoid people making a fuss about Reinforce; I can imagine a few of the arguments myself.
Jill is a definite good rank; she's got some minor plot here and there, and is a very popular character. I'd actually support ranking Haar as well for the same reason, and the Brave Axe I'll let him have along with stat differences mean that they won't be carbon copies of one another.
Mia is... um, technically a GM I guess? Plus we need a swordmaster. Nephenee, Brom, and Kieran are all in the same boat basically, except that Brom isn't used quite as much as the other two, and Kieran shares his class with oodles of other characters, so Nephenee gets to represent Halberdiers. Astrid can show up, fine.
Ranulf seems like the best Laguz rank, and I wouldn't mind throwing in Lethe and Mordecai as well. I could be convinced of Janaff and Ulki, though no one seems to like them much.
Tibarn and Naesala both have lots of plot. Both have potential FE Godlike hype, which is awesome, lots of plot, and forced appearances.
As for bosses, Petrine, Oliver, and Ena are the most significant bosses that don't have major issues. They all have plenty of plot, non-controversial abilities, and I like FE bosses more than a lot of the PCs. Black Knight is an obvious no regardless of any goddesses (superbossy duel), but I... think that Ashnard might be doable? I'm not convinced that people in general would let him null most of the attacks in the DL, and hard mode interpretations can theoretically affect most bosses (Mithos getting Indignation Judgment for example).
As for anything missed... A straight no to Illyana, Zihark, Sothe, Makalov, Tormod, Muarim, Stefan, Devdan, Reyson (yeah...), Callil (T_T), Tauroneo, Largo, Nasir, and Giffca. Bastian, Lucia, and Geoffrey all have some marginal end game plot to go on, though none of them are unique to their class, so I'm on the fence with them.
To summarize:
YES: Ike, Titania, Oscar, Boyd, Soren, Mist, Volke, Ranulf, Elincia, Ena, Petrine, Oliver, Tibarn, Naesala
Maybe: Rhys, Shinon, Gatrie, Rolf, Mia, Marcia, Lethe, Mordecai, Nephenee, Kieran, Brom, Jill, Astrid, Tanith, Janaff, Ulki, Haar, Bastian, Lucia, Geoffrey, Ashnard
NO: Illyana (T_T), Zihark, Sothe, Makalov, Tormod, Muarim, Stefan, Devdan, Resyon, Callil (T_T), Tauroneo, Largo, Nasir, Giffca, Black Knight, and anyone else I missed, unless someone wants to start hyping Seeker, Bertram, or Homasa >_>