Wessie's advice is wise; always closely examine a busted tube after removing it. The culprit could be obvious, but you'd be doomed to flat after flat if you don't investigate.
Assuming you're installing the tube and tire carefully and correctly, there are a few basic problems that can get ya repeatedly. Always, for instance, run your fingers along the inside of the empty tire after a flat -- if the problem was a standard puncture or cut, the offending bit of glass or rock could still be lodged in there, waiting to nail you five miles later. As others have mentioned, inspect the inside of your clincher rim for evidence of a sharp spot; the area around the valve hole is sometimes messily drilled.
Of course, all of this detective work is much easier when you've got the corpse as evidence.
There are some basic steps to follow during tube installation that can make pinch-flats less likely as well. One particularly anal step that can help: once the tube and tire are seated, pump the tube up to 30 or so psi, and release the air out. Repeat once or twice. Think of this as applying tension to the tube on and off, popping any twists or kinks out, and reducing the risk that any limp sections are caught beneath the tire bead. Again -- not a necessary step, but an anal one worth following if you're troubleshooting multiple flats.
The other step you should follow every time you install a tube is to pull the tire to one side and peek down in the rim to insure no tube is smooshed or popping out from under the bead; follow the tire all the way around the rim, flip the wheel over, and check the other side. This isn't something you'd do in the middle of a race, but again, in the interest of reducing your flats, something you should do regularly in normal situations.
Good luck, and let us know how it goes.
