Cut and replace
If a cap doesn't twist free, and the cap is metal, not plastic, heat the cap with a heat gun and grip it with the bare teeth of a slip-joint pliers.
If heating doesn't work, or your faucet is plastic, cut the cap with a rotary tool and a cutting wheel. Then jam in a flat-blade screwdriver and widen the opening until the cap unscrews. Buy a replacement cap at the home center. Coat the new cap threads with plumber's grease to prevent it from sticking again.
Get aggressive with setscrews
If the hex wrench that comes with your repair kit won't loosen the setscrew on the faucet, don't force it—you'll just ruin the head. Spend a few bucks for a 3/8-in.-drive hex socket kit. Buy a tube of valve grinding compound and apply a dollop to the hex tip to reduce the likelihood of stripping the setscrew. Then use a ratchet to break the screw free. If it still won't budge (and the handle is metal and not plastic), try heating it with a heat gun. As a last resort, drill out the center of the setscrew and use a screw extractor to remove the rest of it. Buy a new setscrew and coat it with anti-seize compound before reinserting it.
Special tools are worth it
Replacement cartridges usually come with a plastic loosening tool. If the cartridge is really stuck, the loosening tool can actually break off the cartridge ears and turn the job into a real nightmare. Even if you get the cartridge to rotate, you may still have to yank hard to get it out. Save yourself a lot of time (and sweat) by forking over a few bucks for a cartridge puller from amazon.com or a home center. Install it and pull the cartridge in minutes.
Know when to throw in the towel
It makes sense that a pivoting kitchen spout will leak if the O-rings are worn. But brass wears too. So if you've replaced the spout O-rings and the leak reappears in a few months (or weeks), check the inside of the spout.