If you want to avoid flats and don't mind the weight penalty you should try schwalbe marathon plus tyres. They come in all sizes, 700 and 26", from 25mm up. I have used them for touring for over 8000 miles now and have had only one puncture. As a result I have put a set of 700x25s on my fixie for riding around town.
I wouldn't use them on my road bike, they're heavy and they aren't as good as a racing tyre when cornering hard, especially in the wet. But for general purpose cycling/training/touring they are amazingly durable and puncture-resistant.