I generally create all the music and sound for my game projects. I use a very wide variety of software for audio, from FLStudio, the freeware Jeskola Buzz, and Orion Pro among others.
If you're just getting started, I could recommend Audiotool.com
, which is a free site that provides a very robust and powerful audio composition software, utilizing Adobe Flash. An avid user by the name of hlecktro has a number of videos posted to YouTube that you could use to get an idea how it all works.
There's also SunVox
, which is a freeware, modular tracker software that has a number of synthesizers built in that really work well for games. The creator of SunVox has a YouTube channel where he's posted a bunch of videos to help you get started.
There are scores of other softwares out there, free and commercial. If you're really serious about audio, I'd advise taking a good look at KVRAudio.com
. They're an invaluable resource for audio production.