Finale Notepad is free, and it can export to wav.

I like Aodix. It is very powerful and does not rely on MIDI things at all. There are plenty of free instruments around the net for this one. I particularly enjoy its ability to use the normal keyboard for note entry since I cannot afford a dedicated musical keyboard. It can't export into wav though, rather only into raw pcm data. But things like Audacity can convert it to anything you'd like.

If you are feeling adventurous you can also try Direct Music Producer... That is if you don't mind WGA business. I found it quite nice too and easy to use. Entering notes here is reasonably easy as well. This one uses MIDI's and you can easily create new instruments from recordings. It can export into wav.

An old one is ModPlug from their website. It's the first one I've used; I've never heard of Finale Notepad, though, so I may have to change my preferences if, after I look it through, find that it's better. But there are a lot of good songs made (they have a forum for music people have created) that I like to download and listen to on occasion.

Reminds me of this.

I think powertab is pretty awesome.

though its limited to guitar music, its still a very nice program.

FL Studio Producer Edition is worth its price.

Reaper's not bad either but it's nagware.

I think there are probably some vst plugins for soundfonts. If you have flstudo you can purchase their soundfont player, it's like $40 or something but I think it's worth the price considering the soundfonts I use.

A lot of answers, a big thank you goes out to everyone.

Fruity Loops/Power Tab
I took a look on that earlier. I really like it, but what I dislike is that it's not free.

Sequencers/Aodix/Modplug
I have already downloaded sequencers. I ended up in sitting in front of big grey windows with a huge amount of cryptic numbers. No documentation, no explanation on how to use the software. So after I understood the principles of sequencers, I could alter the given values of the example files, but I was far away from creating my own songs. Being so frustrated I decided to remove it again.

Buying a Mac
If you would know my personal opinion about Macs, you would have never posted this

Finale Notepad
Seems to be professional. What I dislike: In order to get a free copy, I have to tell these guys too much personal information. Asking for an email-adress is okay, but for what do they my telephone number? Exorbitance.

Soundfont
Never heard of that. I think I have to take a close look for it to say something constructive.

@composition software: Pretty much all music software falls into one of the following categories:

1. Notation. Finale is pretty much industry standard on this, and a useful version (printmusic) is available for something like 200€; Sibelius is said to have grown into something useful as well, though the last version I tried was horrible. For free software, the only thing I've found so far (other than Finale Notepad, which isn't really free, and so feature-free that it hurts) is Lilypond - a LaTEX approach to music notation, resulting in a horribly steep and frustrating learning curve, no playback facilities whatsoever, clumsy editing, no WYSIWYG, and a lot of other nuisances. It's almost like programming half the software yourself. The result looks OK, though, but just paying for proper software is arguably cheaper.

2. Multitrack audio recording. The professional ones (Logic, Cubase, Sonar, and apparently FL Studio) come with MIDI capabilities, too, so it's pretty easy to combine recorded audio, actual MIDI, and MIDI through plugins using these. They can all export to digital audio formats such as WAV or AIFF. I use an ancient version of Logic - the last windows version, unfortunately: All versions after 5.5 are Mac-only. Logic can also import soundfonts into its built-in software sampler and insert it into the mix, just like any other audio source, which allows you to mix midi streams on-the-fly and sample accurate. And since it's a plug-in, you can load multiple instances of the sampler, allowing for multiple soundfonts being used at the same time. Other packages probably offer similar features.
There's also ProTools, but that's said to be very expensive and have a very short lifespan due to proprietary hardware. None of these programs I know of prints sheet music in any satisfying way.
And then there's Reason: Not technically a recording program, but rather a modular audio suite. It is used mainly for live performance and such, but using the right modules, it can be a nice tool for all sorts of audio production, including composition.
For free software, the standard one would be Audacity. Far less features, and focusing on audio recording, but then, it's free.

3. Trackers and MIDI sequencers. There is a lot of free software around in this category, but few support VST plugins, and even fewer can do full-fledged mixing, mastering, sampling etc.

4. Stand-alone audio editors. Again, a few free ones are available, but most lack important features.

So it all comes down to your needs. If you want to 'compose' as in 'invent music and write it down for others to play', then you need notation software - but if you're somewhat piano literate, pen and paper will do fine. If you want to 'compose' as in 'produce audio', then you need some sort of studio package - probably a good multi-tracker, but maybe something like Reason is more your style. Don't expect good results from entering notes the traditional way, though: In my experience, "piano-roll" works much better, because it gives you more control. Or, better yet, hand-played.

I'm writing my own midi sequencer and using lilypond to output scores if I feel it necessary. It's pretty nice but I have a lot of work to do before it's practical for use.

Modplug should have a starter kit that has a tutorial that teaches you to use MODPlug to make a quick little song. MP is fun but I'm toying with Finale NotePad 2k8.

lilypond is very good, except that it lacks a nice gui.