Try loosening off all the wheel nuts but leave them on a couple of turn, jack the car up but leave a little weight on the tyre (sitting on the ground), then grab the top of the tyre and try and move it in/out from under the guard. If it's real bad, take all the nuts off first and spray liberally down each stud with something like WD40, try removing the centre cap and do the same around the centre, leave for some time to soak and then try the above method again (with the wheel nuts back on a few turns).
Failing that, just take the whole car to a tyre shop and let them sort it out.
Can park the car against a curb, loosen all wheelnuts (don't remove) then start the car and move the steering wheel left to right until it comes free. Otherwise loosening the wheelnuts and rocking the car side to side can also work. Don't like using hammers or kicking wheels when under a car.
With subborn wheels, I leave 2 or 3 wheel nuts on about 2 or 3 threads and using a nylon style hammer, with the wheel off the ground, belt the inside edge of the rim, whilst spinning the wheel...Sometimes it takes a bit, but persistancy pays off.
And for future reference, I clean up the hub and put grease all round it, before putting the wheel back on.....Saves the wheel sticking again
Happens to me quite a bit. Rears seem to stick most. The centre bore clogs up with dirt. More so for me due to dirt roads. Agree as above clean up the wheel and centre hub once you get it off and apply some grease. I have sometimes had to kick the tyre. The first time i had the issue it was a bastard, hammer and kicking didn't get it. I used a three jaw puller in the end which made light work of it.