I'm a VIM user so I do buy the no-mouse manifesto. I do everything without a mouse and am more productive this way. OSX is not being very friendly, though. How I'm supposed to navigate through files and adjust windows without a mouse? The Finder is very mousy and there's no good way to substitute it.
This question is pretty open-ended, but here's a small sampling of stuff that I use.
For more "heavy" operations, I turn to the Terminal, but it's actually fairly easy to use the keyboard to traverse the Finder. The arrow keys do what they normally do, but unlike Windows, enter renames the file, so you need to use Cmd+down to activate the selection. (Open a file or go down into a folder.)
Another shortcut that's invaluable for keyboard users is Cmd+Shift+?, which allows you to trivially search through the menubar items.
I also use Alfred extensively to switch between programs, both through the main UX and also by using Alfred's hotkey setup. I've also been playing around with Slate for window management, but that has been less of a priority. Lastly, the Pentadactyl Firefox plugin is vital to avoid the mouse (on all OSes).