Not all phones use a Sim card. Here's a link to a picture of one:
http://tmobilesimcards.files.wordpre...t_and_back.jpg
The two small cards at the bottom of the pic are sim cards. The large card at the top is about the size of a credit card. The sim card carries data that identifies you to the cell network, and can also store data from the phone, such as phone numbers. Phones may also have a small removable memory card that stores data, as well as internal memory that stores it. If you remove the battery cover you should be able to see the sim card and the removable memory card, if your phone has one.
I agree with the previous poster. The typical cell phone isn't going to have much information on it that would be useful to an identity thief. And since you always have the risk of losing the phone, you really shouldn't put anything sensitive on it in the first place. While it may be possible for someone to get your data from a discarded phone, the difficulty of doing so coupled with the slim chance that there's anything interesting on there makes it unlikely that this would occur.