I'm the idiot of the year. I kept getting snake bite flats in my rear road bike tire. I got a flat every 15-20 miles. It was incredibly frustrating.
I did some reading on this forum, and I came up with a solution. I bought a tire pressure gauge, since I had never actually checked my air pressure. And I replaced the back tire with an Armadillo tire. I've only gone on a couple of rides, but I'm 100% positive this has solved the problem.
Here's the kicker - my previous air pressure was about 30 psi!! I just tested to see if the tires felt firm, and off I went. Yeah, that's just a few psi short of where it should be.
OK, now you guys can get a good laugh at my stupid newbie mistake. And hopefully me writing about it will save other newbies a few flats.