I second this. I've been taping my mouth closed at night for the past year, and it has improved my sleep dramatically -- completely eliminated my snoring and drooling.

I found surgical micropore tape to be best. It's cheap, breathable, and easy to obtain. From trial and error, my two main recommendations are to first apply it to the back of your hand to reduce the adhesiveness, and fold a corner over before applying. Both of these make it much more convenient to remove, particularly if you need to do so in a hurry (e.g. needing to sneeze).