What could cause the light in my garage door opener to stop working?
Garage door openers are subjected to a lot of vibration in normal use.  There are even special garage door opener incandescent light bulbs which have a stronger filament than usual, to resist breakage from shaking.

Since you've tried different bulbs, the next most likely issue is a bad connection at the socket.  It could be in the socket itself.  There is typically a little metal tab or "tongue" in the bottom of the socket which contacts the base tip of the bulb.  If that is bent down too far, it won't touch the bulb and light it up.  You can check this with a volt meter to see if you have power between it and the sidewall of the socket.  If you have power but no light, this is probably the problem.  Unplug the opener, and reach in to the socket with needle-nose pliers and pull the metal tab up, to make better contact with the tip of the bulb base.

Also, check the socket for rust or corrosion.  If you have any, you can sand it clean with a little sandpaper.

If you check with a meter and don't have power at the socket, then you may have a broken wire or wire connection to the socket.  You'll have to unplug and open up the opener to inspect the wires.