They're usually interchangeable. One slight difference is that "have to" might be the better choice to communicate that what you have to do is an unpleasant task.

Yes I agree with Jonathan. They are more or less interchangeable. However, I would say 'have to' is used more when there is an external obligation and 'need to' when the obligation comes from yourself.

For my part, “I have to…” is objective, it emphasizes on compulsivity. “I need to…” is subjective, it means something is necessary to be done or you cannot successfully achieve what you want.