Others have documented the issue very well. Off the top of my head, it could be one of these three things:
1) The neck is bowing outward. It could be caused by the construction of the guitar, the tension of the strings, the humidity of the environment where the guitar is stored or some combination of those things. Unless you know a lot about the construction of your guitars and have the right equipment, it's probably best to go to a guitar place to get it repaired. If humidity does end up being the problem, most music stores offer sponge-based guitar humidifier for fairly cheap. For more drastic cases a trick is to open-stand your guitar in the bathroom while you take a shower. (Make sure not to get it directly wet, though)
2) The frets were made or positioned unevenly and the string rubs against it. Again, unless you know what you are doing, correcting this should be left to people who are able to take the right measurements
3) Your strings have too little action. Low action basically means that the strings are very close to the frets so you don't have to push very far to make a good contact. This can be achieved by shaving down the guitar's bridge and nut. It's great if you want to play fast, but may lead to your problem if the surgery done by someone inexperienced.
I had the exact same problem with my cheapest classical guitar. It was probably a manufacturing defect and the guitar wasn't worth the price it would cost to get the issue repaired. Instead of shelling out the cash I took two small pieces of paper, folded them up, and tucked them in at the bridge and nut under the affected strings. My problem arose about 18 months back and the guitar has been playing fine ever since...