I have one that is particularly heavy...I don't remember what brand it is, but the directions that came with it said scrape and rinse with boiling water if necessary. The boiling water seems to get rid of any lingering flavors that I might not want in my next food item. (i.e. pizza to breakfast bread)

Not only do I not clean mine I don't take it out of the oven. It's on the bottom rack of one of my ovens and I leave it there primarily because of the way the oven cooks with it. Not to mention I get less cycling (thermostat) which translates to even heating and retention which is always good especially for baking.

No soap, as others have said, it will sink into the pores of the stone and make your food taste soapy. Like others, I usually don't even rinse mine, just scrape off any big chunks, and wipe with a dry rag. I also leave it in the oven during the self-clean cycle. That does 2 things, helps to get rid of any tough crud, and also really helps with the seasoning of the stone.

I never clean mine. Just scrap off any burned bits and it's good to go. I think it's even better used a couple of year. I wouldn't put water on it. But if you must let it air dry first, then in a warm oven for a couple of hours. Stone can absorb moisture and cause cracks when heated at pizza temps. Some cookware shouldn't be pristine and gets better with age and use.

Just scrape off any cheesy pizza gunk when the stone has cooled some. If you must, scrub with hot water and a soap-free scouring pad. No soap ever!

I never wash mine with soap - I try to scrape any stuck on goo off with a metal spatula and rinse in hot water. I figure the oven heat kills any germs