General music, game or non-game related, I use Cubase LE (I'm still in the process of learning how to use it, sort of), which came bundled with my Lexicon Alpha unit.
If I just want to slap together a simple midi, I use Power Tab Editor. It is, for all intents and purposes, a tablature editor for guitar or bass. But it has a feature that allows you to play a midi of the song you've tabbed out, so you can see how it sounds. You can also change the sound of the instrument during playback to, say, a piano or koto etc, and then export the midi itself. It does take a little bit of general music knowledge, such as notes, rests, rhythm slashes, etc.
If I just want to slap together a simple midi, I use Power Tab Editor. It is, for all intents and purposes, a tablature editor for guitar or bass. But it has a feature that allows you to play a midi of the song you've tabbed out, so you can see how it sounds. You can also change the sound of the instrument during playback to, say, a piano or koto etc, and then export the midi itself. It does take a little bit of general music knowledge, such as notes, rests, rhythm slashes, etc.