Here's a really fast, simple, and best of all free way to check whether or not your remote control is working and all you need is a webcam. This trick only works with infrared remotes, not UHF.
Normal remote controls use an infrared LED to flash a light pattern which is invisible to the human eye. The sensors in webcams and camcorders are sensitive to infrared light. Many cameras have infrared filters but they still let a fair amount of infrared light through.
Step 1: Point and shoot
If your remote is hesitant or only works every now and then you can point your remote at a webcam. If the remote's batteries are good you'll see the LED flash brightly while you are pressing a button.