As I see it, there are two options: Get used to changing flats, or get puncture resistant tires.

The first option is really pretty good. Changing flats is not a big deal, and after you do it a few times it becomes pretty routine and doesn't cause too much stress. It turns from "I had to change a flat! " to "I had to change a flat! " pretty quickly. Actually, there are times when it's rather relaxing - I remember riding over Trans Mountain Road (El Paso if you know it) and had a puncture pretty close to the top. I changed the flat (replaced tube) as I watched the sunset in the west - enchanting.

The second option -- Several tire companies, one that I have used, make puncture-resistant tires that work. Continental has their Gatorskin, plus a line of tires with what they call their "plus system". This is what I use - I currently use Continental Touring Plus and have used Continental sportCONTACT, (or SPORTcontact I don't remember lol) and have not had a flat since the summer of 2008 - 6-1/2 years @ app. 1500↑↓ miles per year. Schwalbe Marathons are rated equally as strong although they are a little more expensive. If you absolutely hate changing flats, this is the way to go.

But I like Machka's answer - probably the best thing to do is just get used to doing it, because it's part of bicycling.