OK, so much to address. I say agreed on the fact that stickiness inside the tire is bad. If you're having frequent flat problems, do two things (both cost $, sorry):
If you don't already, get a good floor pump with a pressure dial. I fill my slicks to 115 to 120 psi, and check the pressure (top off really) every day, or every other day.
If the problem is glass and whatnot, look for a pair of tire scrapers. I got them from Via Bikes in Philly
http://www.bikeville.com/ for about $5. They are essentially wire curves, attached at the drilled brake hole (if you have) that follow the cross section profile of your tire without touching. If a piece of glass is embedded in your tire, it gets kicked out before one full rotation. The glass flats aren't one shot deals, the glass gradually works its way in with successive rotations. I'll get some pics going when the camera comes back from the infirmary. I'm not the only one who's heard of these, am I?