If and when I go on an actual paid shoot, I carry lots of excess gear that I might need. I have a couple of old "Halliburton" style foam lined suitcases that I put the stuff in and pay someone else to carry and watch for me. I'm sort of an old fart now, I used to carry stuff myself, but now even a medium weight camera seems heavy after a half an hour or so.
I carry the actual camera I'm going to use in my hand. Maybe another camera with another lens around my neck. A few odds and ends in my pocket during the shoot. An extra battery, film or memory cards in my pockets.
If I'm just going to screw around in the streets of NYC and take photos, I will use a plastic shopping bag to cover the camera and stick it in whatever bag I have my other stuff in that day. One, or maybe two at most other lenses in my pocket or bag. If the bag feels too heavy before I leave the apartment, I take something out before I go.
If I travel, I would not be caught dead with any sort of camera bag. (or "faux" camera bag, or "sissy" bag). Something like a Billingham bag makes you stand out instantly as a doofus or someone who is saying "I'm in unfamiliar territory, please rob me or cheat me". In fact, I like to travel ultra light and I just take a super light pocket camera, with no bag or "tourist" paraphernalia at all.
MAYBE, once in a while, I take an R-D1 or a Leica, but who wants to worry about an expensive camera on a trip? Most of the time it stays in the room safe anyway. If you have a girl you picked up in the room, don't open the safe anyway, and put your wallet, passport and cash in there too.