Big awards - They've won some Grammies. Block Rockin Beats for Best Rock Instrumental, Galvanize for Best Dance Recording and Push The Button for Best Dance Album.
Other big awards that have honored the Chems like Brit Awards, and they've also won Q Awards.
MTV and Europe MTV have also honored the Chemical Brothers.
I'm sure they've also won several other awards as well but I don't know where to begin with that one without doing some mad, time intensive google excercises. You'll just have to do some digging for exact figures/songs/albums. If I come across anything else later on, I'll try to come back to this thread and post my findings here.