The comments on yesterday's monster PCs post reminded me of another issue: the difference between starting with a monster PC and taking over a monster henchman. How this is handled, as Koren suggested, is very campaign-specific.
First, some terminology. Traditionally "monster" in D&D meant "any potentially dangerous being" and could include humans, but in Stuart's original post, the term "monster" is being used differently, more like the non-RPG sense of "dangerous non-human". Perhaps we should distinguish between "character races", "savage races", "alien races", and "monstrous creatures". "Race" in this sense means a human or non-human culture that interacts with other cultures, not necessarily on friendly terms; the campaign's main civilization has political responses to other races, like trade, alliance, strained relations, or warfare. Character races are those that are open to players by default, while savage races are generally not welcome in the campaign's civilized area, but are otherwise comparable. Alien races might not have regular relations with the civilized world, or may even be considered lost or imaginary. Monstrous creatures are not generally regarded as a unified group, but as individuals.
Justin mentioned the example of taking over a gnoll henchman after his adventuring party suffered substantial losses. If any player can choose to begin the game as a gnoll, especially if they are considered a well-known species and culture, you could consider gnolls to be a character race. If gnolls are not standard, but a player can choose to start as one with GM permission, then gnolls are a savage race; they will be treated as outsiders. If the GM disallows gnolls from the start because they're too weird and perhaps only a whispered legend to most people, then they're an alien race, and if they don't really form a distinct culture at all, they're a malign creature.
GMs might allow players to take over a henchman of an alien race, but might forbid taking over malign creatures (such as vampires or dragons.) On the other hand, an accident with a cursed scroll of Polymorph might turn an existing character into a dragon. I've never heard of any GM who took over player characters when they were polymorphed into dragons or mind flayers, so there's some argument that any "monster" is potentially playable. I would argue that it's not really the power level in these cases that's the issue, but the access to secret knowledge from alien cultures or monstrous individuals.