All modern browsers have extensive keyboard shortcuts:
I tested every shortcut, and here's my list of keyboard shortcuts that work in all browsers – or, for the rare keyboard shortcuts I found especially useful, those that work in at least two of the above browsers.
Standard toolbar buttons
Alt+←, or Backspace
Alt+→, or Shift+Backspace
Alt+D, or Ctrl+L, or F6
Ctrl+Tab, or Ctrl+Page Up
Ctrl+Shift+Tab, or Ctrl+Page Down
Ctrl+W, or Middle Click tab, or Ctrl+F4
Ctrl+Left Click, or Middle Click
Ctrl++, or Ctrl+Mousewheel down
Ctrl+-, or Ctrl+Mousewheel up
Ctrl+E, or Ctrl+K
F3, or Ctrl+F
While it's not a keyboard shortcut per se, also note that left-click-and-hold on the forward and back buttons will show a list of the last (n) pages to select from, if you want to go forward or back more than a single page at once. This comes in handy at least once a week for me.
It's good to see browser developers standardizing on at least a few common keyboard shortcuts rather than making up their own.