[dmacvittie]

int is a "low-level" or "base" data type. There is no class associated with it, it is just a space in the computers' memory (in the case of Java in the JVM's memory).
Integer has all of the class information you would expect - you can inherit from Integer, etc.
For me, I only use Integer where I need a class (for storage in lists, etc)... There is a small amount (really, very small) of overhead using Integer, so if I don't have a good reason to, I don't.

Hope that helps.
Don.