It's almost impossible to use most modern apps without using a pointing device or sausage, but a new browser out today is focused entirely on surfing the web with keyboard only. Named qutebrowser, it doesn't just provide a full suite of keyboard shortcuts for the user interface, but generates them on the fly for every link on the page.
qutebrowser is a keyboard-focused browser with a minimal GUI. It's based on Python and PyQt5 and free software, licensed under the GPL. It was inspired by other browsers/addons like dwb and Vimperator/Pentadactyl.