There's also Renoise (http://www.renoise.com/) which is inspired by old school mod trackers. There's a free demo, and the full version is really cheap.
Reaper: http://reaper.fm/ is excellent, very cheap ($40) and has an unlimited trial. Unlimited both in time and scope, you get the full software. I use it, works great.
I personally use FL Studio/Sibelius (FLS trial won't let you save your song in an editable format, but you can export in ogg/wav/midi/mp3). It depends on what you want to do, for music production Pro Tools/Logic Pro are a must (though it's more about the instrument library and external hardware quality).
Overall I'm not a fan, but I come from a background in more complex/full-featured DAW's like Logic and ProTools. I also find the UI lacking. That said, it's a great way to get off the ground when starting out with digital audio.
One really appealing thing about Ableton, if you're just getting into music, is that the UI is simple, slick, and makes sense. The other software has way too much visuals and useless UI pieces. Ableton is direct and to the point. I'm not a musician and have never used "real" hardware, so all that visual overhead in the other programs is just noise.
There's also Renoise (http://www.renoise.com/) which is inspired by old school mod trackers. There's a free demo, and the full version is really cheap.