Chrome: DeadMouse is a Chrome extension that allows you to surf the web with only your keyboard. The idea is simple: if you want to click on a link, just start typing it.
DeadMouse will show you that you've selected the link by making it wiggle on the page. Press enter to choose it, tab to select the next option, or delete to cancel your selection. Watch the video for a demo.
In effect, DeadMouse searches the page for what you type but concentrates solely on the links. It's extremely simple to use, and works very quickly.
In my tests, I wasn't able to follow absolutely every link via the keyboard. Sometimes DeadMouse just wouldn't select links, even when they were purely text. Other elements of a browser window (such as Flash) can take keyboard focus, so this isn't altogether surprising. As such, it's not a totally foolproof solution, but it cuts back on mouse use and is much easier than simply tabbing between links.