First of all, it's a secure element: it allows authentication of the user's credentials with the cell phone. SIMs and smart cards in general provide security at the hardware level as well as the software level (using Triple DES encryption).
Also, they are essential in NFC: that standard is developed around the SIM card and the ISO 14443 standard.
Recent technology also allows the development of Java programs WITHIN the SIM card (it's called a JavaCard: http://en.wikipedia.org/wiki/Java_Card ) and allows to use a single SIM for multiple applications. For instance, you could use your phone's SIM as a mobile wallet, a metro pass, etc...
Of course, as many others have noted in this thread, removing the SIM card would just add the vendor lock-in inside the phone.
Where I live (France), most phones can be legally (or illegally) unlocked to accept different SIM cards.