I haven't exactly given up on My Tribe yet, but after finally sailing to a new island and finding that playing there is exactly like on the first one, I am quickly growing bored with that game. So, following a recommendation from Spinks along the lines of "only Facebook game I don't totally hate" :), I started playing Dungeons & Dragons Tiny Adventures (D&D:TA).
First big plus: D&D:TA is really, really free to play, as in even if you wanted there is no way whatsoever to give them any money or get anything in the game except by playing. There is also no need to spam your friends with invites and "here is a gift, send me one back" messages. All your friends that also play D&D:TA are automatically visible in your friends list. And you can buff them while they are adventuring, or heal them while they are resting, but that is only shown in game, with no extra messages being sent around. The game is "financed" by banner ads for Dungeons & Dragons products. So, by Facebook standards, D&D:TA is extremely unobstrusive.
The second big plus is that the game is relatively close to Dungeons & Dragons in gameplay. You create a character, go adventuring, beat encounters with various ability checks, find loot, gear up, gain xp, level up, and all that in a standard fantasy world with some rather good writing and a bit of humor.
The one thing that will keep most people away from Dungeons & Dragons Tiny Adventures is the time-scale it plays on. Something happens only about every 10 minutes, so a typical adventure with 12 encounters takes 2 hours. That is perfect for logging on here and there, drinking a potion to help inside the adventure, buffing some friends, or going for the next adventure if the previous one is finished. But it isn't exactly action packed. During adventures there is next to nothing to do, except possibly drink a potion, and you can automate that. Between adventures you can buy and sell gear, equip it, and choose the potions to bring for the next adventure. Note that selecting potions isn't just random, there are hints in the FAQ which environment more often does which ability check, and the type of enviroment can always be guessed from the adventure description. And you can also swap around gear to meet the challenges of specific environments. But all in all that still doesn't leave a whole lot of things to do.
Nevertheless Dungeons & Dragons Tiny Adventures is fun. I'm at level 10 with my first character, and once I hit level 11 I'll have to start over with a "generation 2" character, who can inherit one of my items. Further generations open up more character classes and give gameplay bonuses, so there is better long-term motivation than My Tribe has. D&D:TA is certainly not a game you can spend long hours on, but for a quick gaming fix here and there it is very nice. Recommended.