OMG, FarmVille came to mind as soon as I saw the title of this thread, haha. I was shameless about asking people to water my crops. It was so satisfying to "pick" them, too.
I also used to play in a sort of "Facebook arcade" kind of thing around 2007-08, I couldn't tell you for the life of me what it was called, but it was some sort of games attachment thing, and I'd play some version of Bejeweled, a taxi racing game, Pac-Man, that kind of stuff, and I'd try to beat the scores of my other friends who played as well (was successful with Pac-Man

). Was just kind of a nice, temporary distraction from everything else that sucked ass.
Just remembered Honesty Box as well. Not a Facebook game, just another add-on thing, and THAT really wasn't great for the mental health, so... that can stay in the past, lol.