Ableton Live |-> (a serious DAW - digital audio workstation software used for composing, live performance, mixing and recording, post-production, etc., compare it with Cubase |-> and Logic |->) has in the recent years started implementing "audio to midi" feature.
So far it implements the following:
- Melody to MIDI
- Harmony to MIDI
- Drums to MIDI
(MIDI |-> is the lowest common denominator when it comes to recording notes, it's a protocol, a language, a file format and a published standard originating in 1983; the essential thing to note is that by "lowest common denominator" I mean it is a very old format that facilitates interchange of notes between virtually all semi to professional music software, scoring or production)
The most useful of these is the "Melody to MIDI", which assumes "monophonic" (single-voice) recording.
I assume, if you give it a simple enough recording, it will be able to automatically transcribe the notes for you. There might be other "open-source (free or gratis)" solutions out there, but this is in general quite an uncharted territory yet.
As far as "notation" software (which essentially deals with visual aspects of publishing), MuseScore |-> is so far gratis (although somewhat less intuitive than old-time favorites such as Sibelius and Finale |->).
Ableton Live, as opposed to Cubase and Logic, does not provide scorewriting capabilites, and there is quite a good implementation of those in said programs (think of it as "lightweight" scoring functionality integrated into a music recording system).
Thus, the question you are probably going to ponder over is about whether you need more intricate scoring capabilites, whether you need publishing capabilities at all, and whether the creative process is more "theoretical" (i.e. paper and pencil, notation software) or more "practical" (i.e. automatic recording of notes, voices and instruments with recording software).
Post scriptum - Logic (also called Logic Pro, acquired by Apple in 2006) is Mac only, but recently, they reduced the price for the whole package to $200. You get a lot of stuff for that, trust me on that one. So if you own a Mac, and can spare $200, it's kind of an essential music making tool. Ableton Live, on the other hand (as well as Cubase) are both Mac and Windows, so that is also somthing to consider (apart from the price, by which Apple takes the cake, for reasons unknown to me)