I haven't tried them specifically with goatheads, but I've run through nails, staples, glass and just about anything else you could find in an urban environment on Schwalbe Marathon Plus tires.

I have never had a flat over thousands of miles with their Marathon Supremes, either--and they're much lighter and better riding--but they're not as puncture-proof as the Marathon Plus tires.

Neither I, nor anyone in the group of hundreds of cyclists on a local Seattle mailing list have ever seen anything more puncture proof than the Marathon Plus tires.

http://www.schwalbetires.com/marathon_plus

They're available in 700x25, 700x28, 700x32, 700x35, and even 700x38 and 700x45.