Get different tires. I was looking at my rear wheel yesterday and noticed about a dozen cuts and puncture marks in my tire (Gatorskin) - but I've only had one flat with that tire in about 2k miles - and that was a pinch flat from a small but deep pothole that I didnt' see.

As noted here, you can put a lot of patches on a tube. I have about six on the spare tube I keep in my seatbag. Throwing away a tube instead of patching is wasteful, and I like to think dedicated cyclists have better sense than that. IJM is dead right - you gotta let t he glue dry completely. And if anyone out there can feel a patched tube while riding, you must be riding on a road surface made of unobtanium and fairy dust.