I think after 2.5 years of Java you MUST have seen this. Nesting loops is the brute force way to iterate through nth degree arrays when you are doing a blind search for some element. It is the quintessential beginners search method. It is sometimes helpful to know if it is row-major or column-major.
Nested loops are used quite a bit: collections of collections, particularly when recursion doesn't make sense, and any time there's a grid-like data structure being the most common in my experience. It can also be used a lot for XML processing, although often inner loops can (and should) be refactored into their own methods.