I use Bar Keepers Friend on my stainless pots and stainless sink to make them shine, shine, shine. Because I keep my pots on a pot rack and I like them to look spiffy, I use this cleaner on them so I don't have to order out every night.
This stuff removes those watermarks from boiling water too long, the stains from the spoon that rusted in the pot because you were too tired to do the dishes and they sat in the wet sink, and it even works on the bits of burned food that got stuck to the bottom of the pan because you had to walk away from the stove to keep the 1 1/2 year old from dumping out all 5 pounds of flour. The only downside to this stuff is it doesn't keep the dust from coating my pans on the pot rack, but other than that it is great.
Give it a try on your stainless steel pots and pans, but PLEASE don't use it on polished stainless - it WILL scratch. You can find it in the grocery store, hardware store, or even Amazon.com.