Is there a way to spellcheck the word under the cursor with a keyboard shortcut?
If you're on Lion, you can turn on iOS-style spelling corrections in System Preferences under Language and Text. I don't always have luck noticing or reacting to these corrections while typing, but moving back over the misspelled word with your cursor will bring up the iOS-style popup and you can select the correct spelling with the down arrow and Return.

A similar question was asked on superuser, see Keyboard Shortcut to Right Click. To paraphrase that answer here: 


Use Cmd : to activate spellcheck
Focus the floating window with Ctrl F6. (You need "Full Keyboard Access" shortcuts enabled in System Preferences. And unfortunately for me while typing this, Ctrl F6 is already used by the Stack Exchange editor.)
Use Tab and Arrows to navigate and select the right spelling 
Use Escape to dismiss the floating window


You can also "Activate Mouse Keys", but I find that solution unsatisfying.