Well I just really like TF2 for the following reasons:
1) Low system requirements. My computer is nearing 6 years old and it can actually play TF2. That's amazing.
2) Balance. Everyone already covered this, so moving on...
3) Fun gameplay: TF2's gameplay is just fun. Teamwork is a requirement, the stuff are well designed, and frustration levels tend to be much lower than in other games.
4) Great art style, feel, and community: The art style is great. It's probably why the system requirements are low, but it also conveys the humour and style of TF2 greatly. This is also reflected in the community - a lot of the times, you can tell a lot of people are playing for fun and not many are going to bash based on how well they're doing. It's actually crazy how this works out, and certainly adds to the fun of TF2.
5) Lots of support: TF2 gets a lot of support. They update this frequently, fixing up problems and adding in new content. There's been so much for free content (on top of the game being cheaper too), it's amazing. It's just great.
Valve takes their community seriously with TF2. They also make some humourous events as well (Halloween event was FUN!)
Basically, TF2 is great. If you play first person shooters and would like a game that isn't all "super hardcore realistic", you'll love TF2. It's got style, it's got gameplay, but best of all, it's got fun.