You can view the change history of a file by clicking on the history button, or by adding commits to the URL of the file. Here is what it looks like for a file at the Homebrew repository on GitHub:
https://github.com/mxcl/homebrew/commits/master/SUPPORTERS.md
To get a line-by-line history, simply add the SHA-1 string of the commit for which you want to see the diff to the URL after the word commit, and then anchor it with the filename you are interested in. For the same file above:
https://github.com/mxcl/homebrew/commit/288f001e924d5365b79c279e4478f372a04011ae#SUPPORTERS.md
To see all commits for a single branch use a URL like this
https://github.com/mxcl/homebrew/commits/master
To see all commits for all branches use a URL like this
https://github.com/mxcl/homebrew/commits
There is no button or link in the web UI for these URLs, but you can bookmark them easily.