This is a free and powerful open source music notation software package. This program is full featured, unlimited, and works well with a midi keyboard. This platform has a huge community and is constantly evolving. You can also host your music at musescore.com and embed it in a website.
Note flight is a cloud based (completely online) resource for music notation with a free version. This platform is rapidly going and integrated into some educational tools like "Charms Office." One major advantage is a new html 5 editor that works across platforms including the iPad. This tool could be quite useful for teaching composition and the files can be embedded into websites. They also off a paid version that is quite powerful.
Free basic notation from finale. Surprisingly powerful for a freeware program. It will import music .xml for working between different programs. Number of staves is limited.