Lots of people suggesting rim tape -- a good idea.

Also though, carefully inspect the inside of your tire. A piece of road shrapnel can get lodged in the outside of the tire so it pokes into the tire, popping tubes repeatedly. It may or may not be invisible from the outside. Run your finger around the inside of the tire and feel for anything sharp.

On a similar note, a lot of people orient their tires in the same position every time they put them on, in order to make diagnosis of recurring flats a little easier. If your tube keeps popping at the 3-o'clock position (in relation to the stem), you know that either your tire or your rim has a burr at 3-o'clock.