Waking up to a buzzer alarm or loud music is traumatic — doubly so if you get woken up in the middle of a dream, when your sleep is deepest. Ideally, your alarm clock would only go off while you were in light sleep. You can wear EEGs or special watches that do this, but wearing an EEG to bed is a little, you know, impractical. Here's a method for using a music/buzzer alarm-clock to wake yourself up during light sleep, without disturbing a dream.
* Set an alarm to go off before you want to wake up.
* Make the alarm really quiet radio or music.
* Set a second alarm to go off at the latest time you want to wake up.
* Make the alarm the usual loudness.
The whole point is that the first alarm should be so quiet that it will only wake you up if you're in "light" sleep. Waking up in "light" sleep should leave you feeling more refreshed than waking up in "deep" sleep. The second alarm is the back up to make sure that you wake up in time :).
(Thanks, Vincent!)