Sounds like you need to get Slime tubes. Specialized makes a version as well. Or, if you have schrader valves you can buy a bottle of slime and do it yourself. Unable to do it yourself with presta valves.
You need to get a better tire (kevlar beaded) if you don't already.
Also there are plastic inserts (Tuffie I think the name is) you can place in between your tire and tube to help prevent puntures.
I ride in an area with lots of thorns, I just use Slime Tubes and Kevlar tires. Slime adds some weight, but it worht it.