I wish it was that easy.
(A website that automatically tells you.)
But it's really not that hard. Labels are your friends. It will get easier to remember the ingredients over time.
There are websites that have lists of "accidentally" vegan foods, including foods that are vegan that weren't necessarily intended to be, or ones that you wouldn't expect to be. Check out PETA's list at
http://www.peta.org/accidentallyVegan. You'll find a lot of common foods on that list.
Try a little searching online to find other products that you like to read their ingredient labels. It helps to do it ahead of time, so when you go to the store, you already know some of the things that are safe to buy.
Hope that helps.