I do both. "He's staggering badly and bleeding from the gut! 17 HP down and 2 to go!"

That sort of goes with when a player rolls a crit and it's like "54 points! Suck that, monster!"

Hmm, interesting. Well, the way I see it, it's kind of up to the GM and Players to see what works best for them (like pretty much anything else). I can understand the arguments for both and they both seem valid. That kind of takes it into preferences at this point.

I would rather deal with a GM that can describe how badly hurt the monster is based on previous attacks and hit points left, etc.

Hit points are already so abstract when it comes to descriptions so maybe for players new to the system it might be really helpful and make a real difference in their strategy and the survival of the party. Either way, do what works for you...

I think its quite important that the GM describe clearly just how damaged an opponent is, but not by saying "its got 12 hit points left!"; they need to do it in the context of the game.

This was hammered home to me particularly in my Legion campaign.  Its important there because a member of the Legion of Superheroes cannot kill, and some of my PCs do serious amounts of damage per hit. But, they can reduce the number of dice they roll for damage too, basically pulling their punches; so just how much they decide to do in damage is going to depend on getting an accurate idea from me of how badly hurt their opponent is.

I think its fair for a player to ask "is a full-strength blow from my PC going to kill him?" and the GM to answer "in all likelihood, yes".

RPGPundit

I guess it is just... part of the game, but another problem I run into is a player that absolutely can't believe how strong or weak an opponent was.

What about levels then? I like to say, "You can tell by his stance and confidence that he is no match for you," or something like that. Again, it lets a bluffer pretend he is something he isn't.

If you don't mention something like that, how is a player to know how hard he needs to go to win?

My guys are usually clued in when one of them get ripped in half.