The light bulb in my ceiling fan is screwed in so tight I can't unscrew it without breaking the bulb. Any suggestions ?

If the bulb does break you can shut the power off to the ceiling fan and then use a 1/2 potato to jam into the base of the broken bulb to take it out.

Are you turning the bulb the right way to get out? Left to loosen, right to tighten.

In any event I'd suggest cutting off the power to the fan before proceeding as the bulb's base may be fused somehow in the socket due to rust maybe. If that is the case you may have to use a pair of needle nosed plires to remove it and you definitely want the power off to do that maneauver.

Try moving the lightbulb around to loosen the contacts if it still won't unscrew. Push the bulb up towards the ceiling and try and screwing at the same time

Put on a pair of gloves in case the bulb breaks whiling trying to take out. Good Luck

I agree with the gloves first. Be sure it is not a bulb that turns a couple of degrees and pulls straight out. Try towards tightening a hair.
If it breaks, you can sometimes, with power off, to grab bulb shell with needle nose pliers and turn to collapse on itself.

Please put on safety glasses or goggles if you have then. You do not want glass fragments dropping into your eyes.

Or wrap the bulb in a towel so the broken pieces don't fly everywhere or you end up stepping on a piece and cutting your bare foot in the middle of the night.