I removed the lens hood from my camera and the UV filter came off with it. Now they are stuck together. How can I separate them?
There are lens filter wrenches available, such as these, but I find a rubber band works just as well, and always carry a few in my gadget bag. They're also handy for holding a remote shutter release cord or to keep batteries together.
BTW, don't leave a rubber band on the filter, as the rubber outgasses and also may liquefy with age.
Screw the filter back into "something else" - eg less valued adaptor ring, old lens, camera etc - not your most valuable one.
Try varying degrees of tightening then apply a sideways force on hood and undo. You may get a combination where the hood is willing to unscrew first. You may not.
If above fails - Screw onto "something else" as above. Take a scriber or other "sharp pointed hard thing" and press it as hard as necessary and as gently as possible into the joint between filter and something-else. ie at right angles to axis of lens so it sticks "straight out". Not hard enough to stay in position (so you'll need 3 hands) but hard enough to stop joint unscrewing.
Now screw off lens hood.
Now the lens hood is off, throw it away or sell it on ebay or .... .
Screw on hoods are almost always aftermarket items and will often cause vignetting with zooms or when used as universal hoods on lenses they were not "designed" for.
Find a "real" hood. Maybe on ebay. Avoid ones with scriber marks.