I have had a glass top stove for about three years now. I have two spots that have stained black. The stains look like a patch of burnt food, however they are flat to the surface. I have tried to use the white ceramic cook top stuff you can buy (to no avail). I have tried to scrape it off with a razor (also to no avail, and this is why I know that it is flat to the surface of the stove). Any ideas?
First of all, razor on glass is a bad idea. I hope I don't have to explain why. Just think about what you're doing there.
You definitely did the right thing by buying the cooktop cleaner (I assume you used Cerama-Bryte or some similar product), but that's only half the equation; if you just use a cloth or paper towel with that, you won't get good results. There's a product called a "Scrunge" that's specifically designed for cleaning (scrubbing) glass cook tops. Use that with the cleaning solution and it can clean almost anything off.
With a little bit of elbow grease (okay, a lot of elbow grease) I managed to clean off over a year of caked-on grease and charcoal around the burner rings that I was never able to get with the Cerama-Bryte alone. I don't want this to sound like a product endorsement as there may be other, similar kinds of specialized "sponges" on the market, but this is the only one I know of that's safe to use on glass (i.e. won't scratch it like a scouring pad or those double-sided 3M sponges).
You can also try baking soda. Make a concentrated paste (say 3 parts baking soda to 1 part water) and scrub it in as hard as you can. This is often enough to clean by itself, but if that fails...
Finally, you can use the baking soda/vinegar track. Use roughly equal parts of each but don't mix them in advance. Instead, pour vinegar onto the stain and sprinkle on the baking soda afterward, or vice versa, and scrub right away while it's fizzing. That will usually dissolve anything under it.