For lots of American products (at more than double the price of what you would pay at home) you can go to Mega Mart (Salwa Road, between B and C ring). Be aware though, that what is stocked one week might disappear for 6 months. Rule of thumb is if you see something you need, stock up! I hear Shop Rite on Airport Road is also good for American stuff although I have never been there.

I have a list of what I stock up on when I visit the US.... But as time goes on, my list of "needs" from the US diminish. Partly because they start to appear in Doha and partly because I find substitutes...

Good luck!