Can I use an LED bulb in a 3-Way fixture?
Unless you have a 3-way LED bulb (and a quick search indicates that they don't exist yet), it will light, but at the brightest light level.

A three-way incandescent light has two filaments: dim and medium.  Each filament has a separate contact on the bulb's base.  The brightest light level is provided by energizing both simultaneously.  When energized, each filament is driven at the mains voltage, so applying that voltage to a standard LED bulb will cause it to produce its rated light output.

You'll probably find that (because the bulb's base is missing a contact), you'll have an "on, off, on, off" pattern as you rotate the switch, instead of "dim, medium, bright, off" like with a 3-way bulb.