When I joined Facebook some time ago, I had nothing with the games being played on it. The strange wall and all it’s posts from others just felt alien compared to Hyves, where your page is yours own, and others can only comment on stuff or respect (like) them.
A couple of months ago, I was lured into FishWrangler (yep, pun intended), a simple (no Flash needed) fishing game, but with a very large and very active community. When getting the hang of it, I also accepted long standing requests for ZooWorld and FarmVille.
And here I am now, playing FishWrangler with 2 accounts, FarmVille with 2, ZooWorld with 2 and MafiaWars (very nice) on 1. Helping others when they are struggling with how the wall or a game works, and enjoying myself all the time. Well, okay, not all the time: accepting the zillionth Train Whistle for your collection when you already have a surplus of 30 is not always very entertaining, but overall, the games clear the mind and make a very good pastime.
Make sure you have (or make) a lot of FaceBook friends, they are key to the succes of most games. Have fun!