Have you played Sims Social yet? It's the newest version of The Sims and can be found on Facebook. It's a similar format to Farmville or Mafia Wars, in that you can only play a few minutes at a time until your "Energy" re-builds itself. Personally I find that type of gameplay kind of annoying, but... nevertheless, I love, love, love The Sims, so was very excited to try this version.
One thing I really think is cool, and have long wished they had on the PC version, is that you can now visit your IRL friend's Sim houses and hang out with them! You can interact with them and also ask for their help with things. As is the case with other Facebook games, you need your friend's cooperation to pass certain levels.
Other than the social aspect, Sims Social is pretty similar to the PC version of The Sims. You still need to eat, shower, have fun, etc, to keep your Sim happy and functioning properly. (I have no idea if you can actually die in this game. I haven't tried that.) Anyway, everyday life things like that are "free" and can be done at any time. Skill-building and other random things, like mowing the lawn, take Energy, which is replenished slowly over time.