FL Studio

FL Studio is an extremely popular music program. Mainly due to he fact that it's demo never expires. It's fully functional except for the save feature (but you can still export to MP3 at virtually any bit-rate you please), and the demo will never expire. Many people choose to create their music solely with the demo. Some of the packaged VST instruments do have limitations, such as random volume dips, or not being able to save new presets. Some, such as Autogun, are free and fully functional anyway.

The program's most useful features in my opinion are the Step-sequencer, and the piano roll. Both of these make it easy to churn out your own melodies in virtually no time at all. I made my first songs using nothing BUT the step sequencer. You can also import audio files like mp3s and WAVs and arrange them in the multichannel playlist. There's also a video player so you can sync your music as you create it to a video file. However you won't be able to export the video.

There are some VSTs that aren't included with the software that I'd personally recommend myself, such as Vanguard or Nexus. Both demos have audio dips, but they don't occur until about 5 minutes after you load the VST into a channel. Another good program that can be used as a VST (or as a standalone application) is Garritan's Personal Orchestra. This software is intended for Orchestrals, but has been used for a variety of different composition types. The demo page is here. You can download and listen to virtually any of the demo songs in the list.