Tried to make this as un-ranty as possible. That being said, this was produced in a facility which also processes rant, and thus may contain traces of rant.
For those of you who don't know what griefing is, let me sum it up: It's being a dick, usually for one's own enjoyment.
The question was posed a few days ago on reddit, and I so happened to be thinking about it at the time. (Okay, fine, only after I saw the topic)
I'm not entirely sure what drives people to grief others, but my conclusions, some of which were drawn from the thread, are these:
(Note: there are definitely some "reasons" griefers use, but these are rationalizations or post facto justifications which ring hollowly.)
Some men just want to watch the world burn
This is the smallest subset of griefers, I believe. There are those who much prefer to watch stuff get destroyed than make anything for themselves, but the number of people who have this mindset are few enough. Nothing to see here but depraved fellows, move along.
Some griefers get off by doing stuff they know they shouldn't be, getting a rush from the threat of getting in trouble or from the power trip from the illusion of not being able to be caught. Oh, you're such a rebel, killing your team at spawn. I bet all the girls go for you, rebel.
Somewhat like the above, some griefers get off on watching others suffer, or go into grief. Trolls basically feed on schadenfreude but with anger instead of pain. These are like masochists, except with other people. Are we allowed to sic modern "feminists" on them?
This would be a more personal thing, using the griefing as a means of showing how powerful they are. Again with the power tripping. Included in this are a mix of other motives for griefing - anger, jealousy, etc. This is the most childish drive for griefing, revenge, in my opinion, being a very childish thing itself. (Then again, I'm a youth, so what do I know?)
Anyways, being griefed generally sucks; it can turn what could have been a fun afternoon of gaming into a crapfest. (One might even relate them to bullies of the internet) One has to deal with them one way or another, and there really only are a few choices at your disposal (apart from dissolving into a puddle of sulk), and I suggest that all of them be employed.
This one is easy. If you see a griefer, report/ban/kick them or whatever means you have to remove them from the game you're in.
I should preface this with a statement: Chances are you won't make any griefers reform. They're also not worth your time; there are too many, and you're in the game to have fun, not to reform people. So this should be used if you can't get rid of the griefers yourself. Just grief them back until they leave.
"Don't feed the trolls" applies to this pretty well. No reaction means no fun for the griefers. They'll leave.
One last note: generally when griefers grief something, it's something someone else put work into. That is, a K:DR, a Minecraft base, a win/loss ratio, a WoW account, or the like. If you're getting worked up over losing these, as opposed to losing your time, then something is wrong. (I don't mean the time you put into that 10.0 KDR, either. I mean the time you are being griefed) If you need to have a statistic or an object proclaiming how much you love the game or how much time you put into it, you should reevaluate how you play. Think about it: do you enjoy the numbers/achievements/omfgwtfbbqhaxpwn items, or do you enjoy the act of playing the game? Griefers hit the former the hardest, and the latter to a far lesser degree.
tl;dr Griefers are lame excuses for humans, don't even deserve to be called trolls (trolls are funny to other people, that's the difference), but should be met as if they were trolls and ignored.
Addendum: Griefing done "right", just like trolling done right, is funny for everyone involved. To do it "right", it takes a certain level of familiarity, maturity, and cleverness on all sides (at which point it's more like frinedly back-and-forth than malicious assault). On the flip side, griefing done badly, like trolling done badly, just makes you into a childish arse.