If you do a lot of text editing or programing, emacs or vi are both great editors that don't use the mouse. Just open the terminal (or get iTerm while you're at it), and type emacs filename or vi filename. Though, you need to learn a lot of shortcuts to use them.
OS X supports a number of the emacs shortcuts in other applications which is very nice once you know them, e.g. ctrl-a goes to the beginning of a line, ctrl-e to the end, ctrl-f forward one letter, alt-f forward a word and so on.
That said, if you really want to use your mouse less, Linux might be a better choice.
