<p>For obvious productivity reasons, I make an effort of learning and using as many of the keyboard shortcuts for the various Re# commands. </p>

<p>However, it seems that the unit test runner does not have any associated shortcut keys. I want to be able to select certain tests and be able to run or debug them without resorting to grabbing the mouse each time. Is using the mouse my only option?</p>

ReSharper adds items to Visual Studio's keyboard settings dialog box.
Go to:
Tools -> Options, Environment ->
  Keyboard
In the search bar, type "resharper" and see the vast options that you can control with the keyboard.
Specifically, there is one to launch the unit test explorer window, and there's a couple called
ReSharper.ReSharper_UnitTest_RunSolution
ReSharper.ReSharper_UnitTest_RunContext
that are likely what you need.