I don't think they work, period. Not very well anyway. I tried several OTC products without much success and ended up with some sensitive teeth. I finally just opted to go to the dentist and get the custom trays made and a 4-pack of the 15% gel. In just 4 nights, I was probably 2-3 shades whiter. I then got a 4-pack of the 20% (strongest they'll let you take home) and did that a couple times. My teeth are now really white but not "Hollywood" white which I didn't want because it looks too fake.
Yeah, it's a little more expensive to do the trays ($300 for me) but it's ten times more effective than what you can buy at the store and you have the trays forever. So anytime you want to whiten your teeth, you just have to go buy a 4-pack of gel which is only like $25. And once your teeth are established (about a 2 week process), you only need to sleep with the trays in like once every month or so to maintain the whiteness.
The strips are okay if you are on a budget but you'll be much happier with the trays and the strips will end up costing just as much in the long run if you plan on keeping your teeth pretty white.
Just my $.02