We do sometimes, right after he pees... Bee's mom is especially big on letting things "breathe" down there.
Today he was running around sans diaper and he said, "Now I pee" and started peeing on the floor (not on carpet, thank goodness). I stopped him and put him on the potty and he went. It got me thinking that maybe we should let him wear pullups or something.
Well in any case, we definitely have to get serious about potty training since he definitely knows what the potty is and wants to use it but just keeps forgetting.
Do you ever let your non potty-trained LO walk around without a diaper?