With the arrow cursor:
Control + Drag - Duplicates a shape
Press the control key first (Mac OS and Windows) and drag a selected shape or group of shapes to duplicate those shapes where you release the mouse button.
Command/Control Clicking a keyframe to move frame
Command/Control clicking a frame in the timeline switches the cursor to a slider. It allows you to drag that frame to a new place in the timeline within that same layer. This function is useful for editing the positioning of tweens, and so on, in the timeline.
With the magnifier tool:
Control + Click - Toggles to the opposite magnifier.
If the + magnifier (zoom in) is active, and you hit Control while clicking, you switch to the - magnifier and actually zoom OUT.
With the dropper tool:
Shift + Click - Select a color for both fill and outline tools
Clicking a red fill does the same, giving you the Bucket tool, and switching fill colors to red. But the outline tool colors are not changed. Clicking text switches the text tool to that color, and gives you the text tool. Shift clicking with the dropper makes the color you click active for ALL tools. It doesn't automatically switch you to any tool. It leaves the dropper active.
This shortcut is one of the least known for Flash. It's the only way to use the dropper on an outline for example, and then switch to the fill tool and have that color automatically active.