So did both of mine - on my shoulders, in my hands or practically anywhere they could get close.
Since I lived less than a hundred yards' walk from the local vet's surgery when I owned my rats, I tended not to bother distressing them by putting them in a box when I took them for check-ups - I'd just walk down the main road with at least one passenger riding on my shoulders.
It was quite amusing when I stopped at the cash machine en route, and said passengers would poke their heads out of the back of my hair to eyeball the rest of the queue and wonder why we'd stopped.
Once people'd stopped gawking and had the nerve to come close, they were generally quite surprised when I'd take a rat in my hands and invite them to introduce themselves - and they'd find the rats free of sewer odour and extremely friendly.
It's amazing how many people who're scared of or otherwise prejudiced against rats've never actually met a fancy rat at close quarters.
When it comes to animals with a bad press, seeing people score cheap points by repeating old misconceptions annoys me. As has already been said: any animal bite can turn nasty - even from a pet - but death by a bite from a cute, fluffy cat
doesn't tick as many boxes when it comes to phobias.