My most recent flat was on the Horrible Hundred back in November. It was a front flat at about mile 65. I hate front flats because the bike handling gets squirrely. I was not able to find the cause of the flat. It might have been a piece of glass that punctured the tire and then flipped out of the tire. I always try to figure out what caused the flat. Doing so is important. If the offending material that caused the flat is still in the tire, well putting in a new tube is just inserting a new sacrificial victim to the flat tire gods. The tire has been fine since then even though it is getting rather the worse for wear.
I carry 2 tubes and a topeak pump. I like the pump because it is a sort of miniture version of the floor pump. I can get a fair bit of pressure into the tire with it. Also, since it uses air, I am not likely to run out of inflating material.
I figure I get a flat about every 1,500 miles.
Also, as far as fixing a flat goes, it isn't hard. If you haven't done it, see if you can find a more experienced cyclist and have them talk you through it. It is one thing to "watch" someone else do something. It is a whole other thing to do it yourself.