I like to fly with southwest where I can because they have great cheap flights and I find them really reliable. I've used them quite a lot, I also like them because I get points.
I also use Virgin America, because I also get points, they have good prices and go where I need them to.
It really just depends on where the airlines go. Southwest don't show up on airline flight comparison websites and neither do some other budget airlines. Go to Kayak and do a search and get some prices and see how much you want to pay and work out which airlines go with your times etc. They are all pretty good.
I think that most of us fly a variety of different airlines depending on times of flights and prices. There is not just one that is always best for all trips.
Jet Blue and Virgin America have become the upscale lower priced choices but they are not always lower priced and don't always go where you want to go at the time you'd like to get there.
Southwest is our internal budget airline that allows 2 free checked bags but it is not my first choice for cross country flights. I'd use it for shorter trips and only cross country if it were very much less expensive than other airlines. You can only see it on its own web site and not on any of the search engines or 3rd party sites.
The other USA airlines like American, United, and Delta all work fine.
I end up using Delta a lot but that is just because it often works best for where I am going.
Basically the three mentioned airlines above are the way to go most of the time.
Southwest will often come out to be the cheapest when they fly between your origin and destination cities. Their fares are usually among the lowest, and then when you factor in their two free pieces of luggage per passenger versus the other airlines often only having one (or zero) and $25-50 per piece of luggage after that, they really come out less expensive most of the time.
Virgin America I've found to be very good as well - they have very nice, new planes with good inflight entertainment. I've not flown Jet Blue personally.
Generally you'll want to compare prices at www.kayak.com, but Southwest is not listed on Kayak so you will want to check their prices separately.
The other large airlines (United, American, Delta) are generally ok.
I fly southwest often but as mentioned above, I use them for short flights only, e.g. LA to Las Vegas or L.A. to San Francisco. They have very few (if any) non-stop flights that go from the west coast (L.A.) all the way to the east coast (NY) so you'd need to 'change planes' in most cases or, sometimes, you stay on the same plan but it lands somewhere in a city midway between the coasts. Stopping/changing can add 2 or 3 more hours to the flights as there is often a layover in between flights.
The other things to remember about southwest is that they use Boeing 737's only (no wide body planes). So, you're looking at a plane with a single, central aisle and 6 seats across. This isn't a big deal if you're flying between, say, L.A. and Las Vegas (1 hour, 10 minutes) but if you fly to NY from L.A., the seating can feel a little cramped.
Add to that, southwest does not assign seats. Instead, you're given a 'boarding #', and you queue up in that order and you only have a choice of seats that are available when you enter the plane. This could mean that you end up at the rear of the plane, or worst case, that your seats end up not being next to one another. This latter condition is unlikely (for the reasons I'll mention below) but it could happen.
Southwest offers an option of 'priority boarding' where, for a fee of around $12.50, you can advance to the front of the queue when you board. If you decided to fly to NY or FL on Southwest, I'd opt for this since the flight would be several hours.
Also, keep in mind, that the 'boarding #s' are assigned when you print your boarding pass. You may do so starting 24 hours before your departure time so if you're diligent about logging in to southwest.com exactly 24 hours before departure and printing your boarding passes, you should get a low boarding #.
Lastly, be aware that L.A. and New York are served by multiple airports. (I'm assuming that when you say "Florida', you're referring to Orlando, right? If you mean Miami, you can also fly into Fort Lauderdale Airport. The alternate airports in L.A. (BUR, LGB, ONT and even SNA) and those in and around NY (LGA, EWR) will give you many more flight options (some of them less expensive than others).
For example, Jet Blue flies out of LGB in the L.A. Metro area and into JFK but they also fly from LGB to Boston (on the east coast, just north of NY) and then onward into EWR. This second itinerary is longer but it might be less expensive.
The one thing I do not like about Southwest, is that at LAX they fly out of the oldest terminal there, terminal 1 and everytime I have been at LAX, that terminal has lines halfrway down the block, so I just avoid that airline although I have flown it in the past, and like HSJ says mainly for shorter flights.
I really liked Virgin America last year, nice flight attendants and seatback entertainment centers where you could also order in-flight food and drinks.
We flew With JetBlue from LAX to JFK a few years ago. I must say that as a budget airline I was very impressed. Leg room was huge and comfortable, compared to say jetstar. Liked them so much that I'm wanting to book them also for our internal flights December/January but as yet those dates aren't out yet.
I am not a fan of Southwest Air, but they do have good prices. As 55 says, that terminal 1 at LAX is always crowded with lines. My cousin flies them every week for work in San Francisco. I can see a guy with just a briefcase jumping on a commuter flight, but we don't care for all the lining up and waiting around to board.
We began using Virgin America for local flights, and we love that airline, usually same price as SW. Have used Jet Blue a couple of times and think it's good too.
My friend flies all the time, back and forth to JFK in NY, and only uses Jet Blue and couldn't be happier.
We are from Australia and are currently in the US and have used Southwest Airlines twice whilst being here. We found them great and on time. The reason we flew with them was because of the free luggage and reasonable flight prices as there is four of us travelling.
I'm flying with my family from Sydney to JFK (via LAX) on Qantas, then internally NY - Vegas via Virgin, then Vegas - LAX on virgin again, because Qantas for the ride home.
I have to agree with the previous posters that flying out of terminal 1 at LAX on southwest involves some long queues. Still, a deal is a deal. Alternatively, I fly on southwest often out of BUR and I find the queues there to be very manageable. The price difference between departing out of LAX versus departing out of BUR is, often, very little and sometimes zero. In those cases, I'd opt for BUR.