From what I know, most cars' need an oil change after 3000 miles of driving. However, the intervals between oil changes will depend on your driving habits and the type of car that you are driving. You should check your owner's manual to know the period after which you need to do and oil change.
I pretty much agree with Clemence. Even though owner's manuals say something like 7,000 miles between oil changes, I think this is way too long to go. But I think you might go a little longer than 3,000 miles, perhaps 4,000 or 5,000 at the most. Twenty or thirty years ago, 3,000 miles was the standard oil change interval. But oil and rings have gotten better now, so I think you'rer safe with 4,000 or 5,000 but no more.