Howdy, I run for a college team, but I cycle twice a week(usually 80miles per week). Here's my question, The last two times I rode, I got flats, one was from a goat-head thorn(not much i can do about that), but the last puncture was a small rock, I know bike tires are thin, but it was a really innocent type rock. My tires have quite a few miles on them, so I'm going to get new tires, (so in a nutshell) what kind of tires should I get that are thick enough so that the dangers of northern new mexico roads don't puncture me when I'm on a 1lane mountain pass road 20miles from town(I had a bad experience last time). Thanks in advance.

Look into getting continental gatorskins, or maybe specialized armadillos, which are heavier than the gatorskins but probably more bombproof. Michelin Krylions are also pretty puncture-resistant; not quite in the same class as the gatorskins or armadillos, but more ridable. Good prices on the krylions and gatorskins at probikekit.com, with no sales tax and free shipping.

Try inserting a Kevlar (?) liner between the tube and inner part of the tire. In Mesa AZ, I would remove dozens of thorn points from the tire when riding in "wrong" areas. Some points were worn down, so I learned to bring tweezers on my rides. Never used goo inside tubes. Anybody like goo?

goo does not work at the pressure that road tires inflate to

Gatorskins and Armadillos trade off a lot of road enjoyment for puncture resistance, so you might start with a tire that makes a compromise, such as the GP4000. Those goat heads are supposed to get through a lot of tires though. I think terryb may have good answers to this question because of his locale.

Goat heads can and will go through most stuff, including the interior kevlar bands at times. The bands can introduce their own problems; beyond weight and reduced rideability, they can also cause flats on their own if improperly installed. Main issue is protecting against all the other stuff out there. The GP4000s or Krylions are probably what I would try first.

Here's what I use on my old touring bikes. Mine are going on 30 years old and are prolly haven't been made for 20 years. They were considered dorky to use in their day but sure keep goat heads from giving you flat tires. Copy and paste from Sheldon's web site:
"Tire Savers
Some punctures are caused by glass slivers or thorns gradually working their way through the tire tread. What can happen is that a small sharp object may be picked up by the tire, then gradually work its way in over the course of several tire revolutions. The pointy thing is driven in like a nail into wood by repeated blows against the pavement. A formerly popular device called a "tire saver" or "flint snatcher" used a loosely spring piece of wire (generally made from a bicycle spoke) to constantly brush the tire tread in hope of dislodging glass slivers and the like before they could penetrate all the way to the inner tube.
These are of dubious value in practice, but may be of help in backward areas where throwaway beverage bottles are still legal, and glass slivers are a major problem."
We used to call them Sticker Flickers. Sheldon apparently never rode in areas where there are lots of goat heads. I do in backward southern NM and can't remember when I had my last flat tire.