Unlike most of the other carriers, Southwest is a bit of an odd ball. It is currently one of the largest carriers in the US, but it goes against the grain in just about every way: No alliances, no fees for changes or checked bags, no assigned seats, free snacks during the flight, and no prices published through the big fare aggregators like Kayak. They do things differently and there is a lot to like (and dislike).
The biggest mental hurdle for me is the no assigned seats. You have to sign in at 24 hours prior to your flight in order to get a decent seat and that is stressful. I like to know if I will have a window or not, and I prefer to know ahead of time where I will be. For most of the people that I have talked with who were not used to flying Southwest, this was a big barrier like it was for me.
Here's how the system works in practice: Southwest assigns two sets of numbers, A and B, both with numbers 1 to 60. The lowest numbers are for their frequent flyers (the "A" List), people who pay $10 to automatically check in, and then after that it is first come, first serve. Checking in as close to 24 hours prior is strongly recommended.
Overall, the flight was smooth. There is no in-flight entertainment on Southwest, so you have to keep yourself entertained, but the snacks that they hand out are better than usual: Oreo's and other Nabisco snacks, as well as generic Southwest mix (nuts, pretzels, etc.) Here's the view from the wing: