I don't and would not (unless there was a real defect).
One, the point at which they consider tires worn out is beyond the point at which I'd change them anyways. I'm not going to drive on shit tires to wear them out completely to get a few bucks back.
Two, chances are that if my tires are wearing significantly faster than they should, it's either due to poor maintenance (alignment, over/under-inflation, springs and shocks/struts) or due to overly aggressive driving, both of which are my fault, and the manufacturer should not have to pay for that.
On the other hand, I paid for road hazard warranty, so I'll take it if it happens (again, if it's not due to my fault, like deciding to drive on a bed of nails for fun.)