Here are some of the bread-and-butter shortcut keys I use most frequently:
Command-Shift-A Deselect all.
Contorl-B Enables/Disables a clip. This is a great one to use when trying to compare clips. Stack one on top of the other and use Control-B to turn your alternative on and off.
Control - and Control = Raises or lowers the audio levels 1db, respectively. Make sure to either select your clip or place the playhead over it first.
F Loads the clip under the playhead in to the Viewer.
J, K, L These are the transport keys. They move you through the timeline. J is backwards, K stops, and L is forward. Pressing J or L twice in quick succession doubles the speed. Also, holding J and K together moves backwards in slow-motion while K and L moves forward in slow-motion.
Keypad 'del' The keypad delete key performs a ripple delete, collapsing the space left after removing a clip. The result is the same as using shift-delete but simpler.
X Marks an In and an Out point on the clip beneath the playhead.
Option-V Paste attributes. First, select the clip whose attributes you want to copy (command-C). Then, paste on to another clip using option-V. Great for pasting size and level attributes between clips.
TTTT or Shift-T Changes the cursor to overlapping arrows. Touch any clip and all clips forward will be selected. Great for moving around large chunks of an edit.
+ and [number] Moves the selected clip forward - to the right - by an increment of the entered number. - and [number] moves the selected clip backwards, or to the left.
For more Final Cut keystrokes, check out my twitter feed @fcpkeystokes where I post a new shortcut every day.