Never hit one but I passed (on a bike) within 5 feet of a fresh-kill carcass a couple of minutes after it was hit. The offenders had parked their car and were standing over it - not sure what their plan was since it's chest cavity was hanging open. Never smelled anything like that before and would prefer not to again.

As for close calls, I startled the same deer (I think) twice in a half hour on my last run. He probably thought I was stalking him.