I usually just put whiners on ignore, but some people are so whiny I just don't think they deserve my tanking love (or healing/dpsing love for that matter). I've had runs that have gone perfectly smooth, no one has been close to death, threat is not an issue, I'm not asking for cc (because omg, that is so much hassle) or complaining about anything, and you can still bet your next salary that someone will find something to whine about. Just the other day I had a run like this in Stonecore and some guy just had to complain about my addon that announces my cooldown usage in party chat. I'm sorry dude, this is part of the bargain. I happen to like it when my healer knows if I've got Shield Wall up in a tricky situation or not, mostly because I know that that is information I would want if I had been the healer. And I'm sorry, where you using the chat for anything useful? Nope, it's completely empty and silent, and I don't care if you have 15 important whispers or something going on in guild chat, right now I want you to focus on our instance. Besides, one shout out every 3 minutes is hardly "spammy". I won't actually kick someone for just whining though, like I said I mostly just put them on ignore. But some people take it to the next level and start complaining about anything and everything. The healer is an idiot, the other dpsers suck, etc. At some point I just don't think he deserves our time anymore and will vote to kick him.
Like I said initially, I don't mind people being bad as long as they try. Because there is seriously few things that annoy me more than people who can't be arsed to do their part of the job. Again in Stonecore (albeit another pug) we were doing the first boss. I had asked the dpsers to take care of the adds, but what do I see? All adds hitting on the healer. I sigh and do some charging/intervening/heroic leaping to pick up the mobs from the healer and trying to avoid getting the buff on the boss, although I failed with that so we wiped. So I ask the dpsers to kindly take care of the adds, why would they just let them stand there and hit the healer? And one dpser asks me "why don't you do it yourself?". First of all - I am taking care of the boss tanking in case you didn't notice. But sure, ok, tanking a boss isn't all that troublesome. Secondly, the fight mechanics prevent me from helping out on the adds unless I want to make the boss hit really hard forcing me to use cooldowns. But sure, that's what cooldowns are for right? Thirdly however - didn't you just notice I was in fact the only one who cared about the adds (which made us wipe when I was out of cooldowns), and you have the nerve to tell me to try harder?
Another matter in laziness that really (I mean really) grinds my gears are people who don't release and run after a wipe. I can understand if when only one or even two people die, they don't release and run. I mean as long as one resser is alive and well, you might save time having them res you instead of running all the way. But when we all wipe, there is nothing to gain from having one person just lie there, waiting for the rest of us to do the running. The only time that is ok is if you happen to sit on a computer from 1995 that has so slow loading times that you actually prefer getting ressed over having to release and run. I've encountered such people and that is totally ok. I even accept people who say "I have to do x, is it ok if you res me?". Just bleeding ask and I will say "sure, fine" and think nothing of it. But just lying there, taking it for granted, will really piss me off.
Not gemming your gear pretty much goes here too. I can understand that people don't want to enchant gear while leveling, but when you're doing ZA/ZG and got epics... it's time to put a little more effort into your gear.
3. Not fulfilling your role
Although I accept bad playing, and I mean bad as in "not knowing your class inside and out and perhaps not bringing 25k dps to my group" generally, I won't allow it to stand in the way of the group progress. If your playing is so bad that I know that it is YOU that are hindering us from downing this boss, I will kindly ask you to leave, get some better gear, read up on your class and the tactics of the fight. I also don't accept people who refuse to use their class mechanics. I will take the time to explain them, because like I said I don't demand that everyone knows everything like the back of their hand. But we're at max level now, you've played that class for 85 levels and you will have to stop making excuses somewhere and start learning what is necessary to know for heroics. When the shaman in VP told me he couldn't bind elements I told him to go train it for the next instance, because people would want him to be able to do that. He then eventually found it in his spell book, no harm done. But the other day when doing BRC I asked the mage if he could kite the adds on the last boss. He said no, he would suck at it. I said that's ok, be as bad at it as you want - as long as you keep the adds of me you've succeeded. I explained how he could go about doing it, basically just frost nova, blink, ice lance to regain threat. It's seriously easy. But he just refused. No explanation. If there is something I don't have the patience with, it's people who won't even try. Now either he thought it was dreadfully boring, and I would've accepted that if we had had an alternative kiter (although basically anyone can kite that). Or if someone else in the group had said "I love kiting those mobs, please let me!". Otherwise it's to me like if the shaman would say "no I don't like popping totems, it's boring" or the priest says "no I don't like using Fortitude, it has an ugly icon". I don't really care - you've chosen that class and spec, so that is your role. People will ask you to do this so if you don't enjoy it, go reroll. I don't mind you doing it badly (as long as it gets the job done), but you have to do it, sorry.
2. People who just fail
I won't mind someone doing bad dps, or accidentally pulling an extra group, or not knowing tactics and loads of things. All of those are ok - but not at the same time. The other day I was doing (yes, I am doing a lot of pugs lately) Lost City and we had a DK who not only did awful damage and didn't know tactics - he face pulled everything in the instance. He managed to pull groups I've never ever fought before in that instance, after having done it some 50 times. He gave the rest of the group so much extra work, making what could've been a really smooth run really troublesome all by himself, that I finally had to tell him that he wasn't worth the trouble. He wasn't pulling his weight, he was instead adding extra weight. Not ok. If you're bad, be humble, try to counter it by being useful in other areas like cc, buffs, debuffs, anything. But just being an extra workload and no gain won't give you much sympathy from me.
The above example is of a fail player that I don't think actually tried to ruin our run, he just did inadvertently. But there are also the players who think they are more important than the rest of the group and that their needs should be put above everyone elses. "Hurry, I've got work in 20 min so we have to chain pull the instance" - sorry, don't care. Don't join a run that takes 45 min when you've only got 20. Don't take it out on the rest of the group by face pulling everything you see so that the tank has to chase after you and the healer go oom after each pull because everyone is taking damage. In any case, that sure as heck won't make the run go any faster.
I think most people agree with me that the biggest asshats of them all are people who shamelessly take stuff from other people. All of the above are things that not necessarily have to be because the player tries to actually be annoying or ruin the fun for other people. But taking something from someone else says only one thing - I think I am better than you, and I couldn't care less about your feelings. In a game that is all about social interaction and teamplay, that is just not ok. Fortunately, the ninja problem has become way less of a problem in Cataclysm than it was in Wrath. Nowadays, epics drop so often that people care more about being able to stay in the instance than getting that 100g that the epic might be worth, or 20g that the blue might be worth. But ninjas are still, without a doubt, the people that annoy me the most in pugs.