It's been a long time ago, but Joel and I were watching a PBS show and it was about tips. And the one that I grabbed ahold of and have found to really work is cream of tartar and vinegar.
If I have a pan that has a stubborn stain, which I have been having more and more often lately, because we bought a stainless steel pan for Advent this past year, then this is the cleaner for you.
All you do is splash a little white distilled vinegar (others would probably work, but this stuff is dirt cheap) and then you sprinkle a little cream of tartar and wipe with a dry wash cloth or paper towel. This will get rid of cooking stains, residual grease, burnt on plastic (don't ask). It's great and really simple to use. I think you can make a certain mixture to soak things in, but I don't remember that.
You can also use cream of tartar mixed with hydrogen peroxide to clean in the bathroom. That stuff is amazing!