As mentioned by unnamed GUEST above, ABC notation is perfectly adequate for straight forward single melody line notation. Being based on a text file, you do not have to do your composing or transcribing on a computer with a specific programme installed, which makes it a very portable system. It takes a bit of learning to use, and if not used regularly the rules can be forgotten, but you can jot stuff down on a piece of paper and then type into a computer when available.
One advantage of ABC is that as long as you can get online, there are ABC converters which will produce both printed PDF and MIDI files from your imput. ABC converters can be found at http://www.concertina.net/tunes_convert.html and http://www.folkinfo.org.
If you need to print out more complex scores, it could be worth checking out Lilypond. This is free software, which like ABC is text based, but designed for typesetting up to full orchestral scores. I haven't realy played around with it properly so cannot comment on how easy or difficult it is, but it is cross platform and FREE.
The Wikipedia page linked to also mentions some Linux progammes which could also be worth you checking out.

I just followed some links which led to http://www.denemo.org/index.php/Main_Page. This seems to be a free, cross platform, graphic music editing programme which uses Lilypond for its final printed output.

Quack!
GtD.