Something often overlooked, but simple to write with regex would be username validation. For example, we may want our usernames to be between 4 and 28 characters in length, alpha-numeric, and allow underscores.
Telephone Numbers - A much more interesting example would be matching telephone numbers (US/Canada.) We'll be expecting the number to be in the following form: (###)###-####
Again, whether the phone number is typed like (###) ###-####, or ###-###-#### it will validate successfully. There is also a little more leeway than specifically checking for enough numbers, because the groups of numbers can have or not have parenthesis, and be separated by a dash, period, or space.