EDIT: Changed the topic title. Was a bit drab and not at all topical.
So. Vetinari is getting on in years, and it's only a matter of time before a new Patrician is going to be needed. A few people are in good position to take it up. Let's look them over, shall me?
Samuel Vimes
The front runner from the "Obey the law or I'll knock you upside the head" party. He definately has the rank and money, as well as the support of the people and respect of foreign powers. Has shown himself to be one of the few people to even come close to understanding how Vetinari's mind works and operates the city. He's off the rolls of the Assassin's Guild, so no worries there. The cons would be that I would think it's too obvious and that he also wouldn't WANT the job, even if given to him.
Carrot Ironfoundersson
The boy would would be king. Definately matured, could easily run the city, and he's liked by the entire populace in varying capacities. It's hard to dislike Carrot. Always good to see a Patrician whose idea of foreign policy is wrestling werewolves with his bare hands. That'll keep the neighbors quiet. Could also see him not wanting the job, but I think he'd be more likely than Vimes to accept it.
Moist von Lipwig
Already shown himself capable of revolutionizing two government institutions, whose to say he can't revolutionize a goverment? He's got the politician's gift of knowing what to say and the flair for the dramatic. The people like him, or at least like to watch him/bet on him. Vetinari seems to have taken a shine to him recently as well. Cons is that he's a big ol' target, a foreigner, and would probably as soon as jump off a bridge than accept the job.
William de Worde
The dark horse candidate from the Intelligensia. Not sure why I'm including him, but he is about the only other person I can think of. Has a fair bit of influence with the Times, though people don't particularly like him one way or the other.
Other
Write-ins always welcome.