I know I am going to make some people upset, but I clean mine for the same reason that I clean my dishes. I dont think old food and crud gives the new food on my plate any character or taste that I want in there. Thats just me, YMMV.
As far as cleaning goes, I like to get to high heat and just burn it off, and then brush the old gunk powder off, good as new. Stubborn stuff might need a grill brush. Thats about it.
John - Salt Lake City, UT