American Airlines is my primary choice when flying. One of the 3 legacy carriers and the largest airline in the world. They fly almost everywhere, and if American doesn't fly to a specific location, one of their code share partners definitely does. I fly a lot for work and also sometimes for vacation - at least 50 times a year, and American Airlines is always my number one choice.
If you're a frequent flyer, then definitely sign up for American's elite status program. It's free, so why not? I have high status with American so I get free upgrades to first class whenever possible, and I can do same day flight changes for free. I would even recommend getting an American Airlines branded credit card to gain miles on everyday purchases.
Customer service is pretty good, I've never experienced any major issues with them. They have awesome lounges called the Admiral's Club. The airports where American has hubs has up to 4 admirals clubs. Delays are minimal, flights are smooth, and service is great. I don't see any reason to change to another loyalty program from American Airlines.