Anything that requires creative thinking. If I'm writing a book I wake up constantly with ideas. Right now I'm designing and building tube amplifiers and I think about circuits during the night when I wake. I also write songs and I ruminate over the structure, melody lines and harmonies. Anything like that. I wake up 3 to 5 times in the night.
One thing that usually sends me to sleep is music, which I play every night when I go to bed. It's usually my gospel playlist in iTunes - I find modern gospel music soothing. Occasionally it will be Bill Evans, Schubert sonatas or Debussy, but the piano is a more percussive sound. Around 5am it tends to be Ravel's orchestral work - Tombeau de Couperin, Ma Mere L'Oye. Sometimes that works, sometimes it doesn't.