When I lived in Phoenix, AZ I had solid tires in my mtb. It was the only way I could keep from worrying about flats when the trails were all rocks and cactus. By the time I left and sold the bike the tires probably got more traction from all the goathead stickers in them than the actual tread.

If you get out on normal roads you can usually do well with normal tires. I haven't had a flat on the road bike for nearly 500 miles/800 km's. I'm running Conti Gator Skins in 700x21. Not quite bullet proof but a good tire for the money.