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 ("flat-less") 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.
Marathon Plus on Schwalbe's main site
Product listing from Schwalbe North America (distributor for North America).
They're available in a wide range of sizes.