Mob Wars and Mafia Wars
Mob Wars and Mafia Wars are very similar games. You are the boss in a number of cities, and each have their different challenges. There are quite a few players around, and you need to build a strong base of fellow gamers to avoid being attacked by large mobs.
Oftentimes, it pays to get in touch with larger families, and ask them to join your mob. Exactly as in organized crime, numbers and money speak the common language understood by all, and you can easily run through the initial levels and meet more challenging assignments as you grow your mobs.
FarmVille
This is a rather fun game where you are your own boss owning a far with animals and vegetables to be grown. You get some very nice gameplay, but the game does lag at times due to quite a few players online. However, if you enjoy the thought of running your own business, this can be a nice way to develop some skills that will be useful for you later in life.
CafeWorld
Just as in FarmVille, you run your own business, but this time the focus is on running your own cafe, and you will get lots of customers when you remember to have fresh coffee available, and when you run a selection of three to four dishes (or more), customers keep coming in. You can build a fortune in no time, and gameplay is rather fun as you are kept on your toes by incoming people waiting to be served.
AirPort City - Free to Fly
In this game you are faced with daily challenges, and running an entire airport is not nearly as easy as it sounds. You can get a good idea of a city simulation, and much like Train City, this is a game that will be enjoyed by all ages.
Conclusion
A very good way to expand your playing experience can be by watching what your Facebook friends are playing. This might give you a very good idea as to what you might also like to play next time you are on Facebook.