Is peroxide safe to use to whiten teeth?

by Carol
(U.S.)

I read somewhere that using Peroxide will whiten (bleach) your teeth. Because I drink lots of coffee, my teeth are yellow. Those Crest white strips work, but they make your teeth so sensitive, and after a while, it hurts my gums to even use them (they are also pretty expensive!) The cheaper stuff with those horrible plastic gum pieces you fill with gel are just to nasty!
Is the peroxide safe? I always mix a bit of water with it, but it Does work.