If something is that important, I schedule something just before. E.g. for a final, I'll schedule an hour of study right before and go to bed early. That way if I'm late to that first thing in the morning, I still make the important event.

The only time I asked someone to wake me up was for an early morning (started at 7 or something) class I took with my roommate. We went together, so we agreed that we'd both make sure the other was up. After that semester, I never signed up for an early morning class again (but I did okay in the class though!).