Sorry to chime in so late, I missed this thread when you posted it last week.
I use the Specialized Armadillo tires on my roadbike (700 x 23C). I really like them. I can't say that I had any great problem with punctures/flats on my previous tires (one per every few thousand miles, roughly) but since going to Armadillos I haven't had any (touch wood).
The only negative comment on the Armadillos I can make is that the rubber seems to be a bit harder, so they do not have quite the same stickiness/adhesion as my previous tires, especially when the road is damp. I've had a few close calls where the rear tire has dropped out on me while braking and cornering, but that's only happened on wet roads. [And yes, I ALWAYS where a helmet.] But this is unlikely to be a problem for a mountain or hybrid bike.
Windmagic, you can skip the rest of what I have to say on this topic, since the rest is just general comments on tire pressure, flats, etc. I mention the following for anyone else struggling with flat tire problems.
As others have said, one of the most important things you can do to prevent flats is keep the tire pressure high. You can't guess at this by giving the tire a squeeze -- you need to use a pressure guage. Roadbike tires may feel firm to the squeeze at just 60-80 psi, but they often need to be in the 110-120 psi range.
If you haven't invested in a good pump, they are well worth the money. Little portable double action hand pumps aren't worth squat. You just can't get the kind of pressure you need out of them. Invest in a solid stand-up pump, with a built-in pressure guage, and secure/clamping head [I have this one which I can recommend highly: http://www.specialized.com/bc/SBCEqP...jsp?spid=25946
]. Check the pressure and top the tires off before each ride. You can get a mini CO2 pump/patch kit for quick repairs enroute, the sort that you can fit in the palm of your hand and stow under your saddle.
All that said, if you are expereincing an inordinate number of flats, inspect your rim and tire very carefully to see if there might be a burr in there that is abrading or puncturing your tube. If not, consider investing in a more puncture resistant tire such as the Armadillos mentioned above or other brands of similar design.