Quite possibly the best "budget" airline in the world, the only budget about Southwest Airlines is the prices. I've flown on Southwest Airlines at least 30 times and every time had service miles beyond other airlines. I've flown on dozens of airlines in my lifetime and Southwest is among the top 3 airlines for me, although it is in a class of it's own for the cost.
Booking is extremely easy and if something comes up, Southwest will work with you to try and help you any way they can. I've had to reschedule flights many times, and it has never been a hassle with Southwest. The staff is so friendly and provide all-around great service. Even after 9/11, Southwest has made my flying experience so welcoming that I continually look forward to flying with them as opposed to other airlines, (which I won't name), where I just want to get to my destination as quick as possible to avoid any further annoyances.
The only minor concern I have with Southwest and the only reason I didn't give them a 5 is the limited area they fly. If they did at least the entire continental U.S., I would never fly another airline if I had a choice.
Just a quick fact, their stock option is LUV. You can see that customer service is high up in the chain for them.
Fly Southwest, you won't regret it.