Unless you're wealthy and can afford to hire a sherpa (can I borrow him?), probably the worst thing about traveling with camera equipment is having to haul it around with you. Shoulder bags are great for carrying your gear on and off planes and trains (and never check gear in a camera bag, always carry it on), but when it comes to actually going out for the day shooting, forget it. Camera bags are a big giant clumsy albatross and trust me, if you go walking through Grand Central Terminal at rush hour with a shoulder bag, some poor old lady it going down.
While I transport my gear in a shoulder bag or backpack, I always bring along a photographer's or journalist's vest and each day I transfer the gear I think I'll need into the vest. (If I'm flying somewhere, I don't have to pack the vest since I wear it on the plane.) My primary vest (I own several) has about 20 different pockets and I can easily carry two extra lenses, a pocket full of memory cards, extra batteries, lens cleaning cloths, filters and a dozen other small accessories. It also has a big rear pocket that's plenty big enough to carry a rain poncho (for me) and a few big black garbage bags to cover my gear quickly if I hit a bit storm while I'm out walking.
Most good vests have a number of inside pockets, too, and in cities or when I'm traveling out of the country, I carry my passport and wallet in a hidden interior pocket. There is also plenty of room for maps, airline tickets and train schedules. I can also carry a sandwich and a bottle of water with me anywhere and if I buy a few postcards or a small souvenir, I can toss them in an extra pocket and keep my hands free.
Because you're wearing the vest, you'll never really notice the weight--especially if you're careful to distribute larger items carefully. I can literally spend 12 hours in my vest and while I'm thrilled to get if off when I get back to the hotel, it's completely comfortable. Yes, it might make you stand out as a photographer and I guess that could make you a target of thieves, but you're a far bigger target if you're carrying around an expensive-looking shoulder bag.
When you're choosing a vest, look at several different brands and designs. The one shown here is from Woolrich and I found it on Amazon but I've never tried one. B&H Photo in New York also has a good selection of both inexpensive and higher-end brands. It's tough to judge one vest from another if you're shopping mail order, so if possible, go to a professional camera store or a big sports store that stocks several vests. You might also consider also going to a hunting of fishing supply store like Cabella's since hunting and fishing vests are essentially the same thing (and some are much better made).
Be prepared for being at the receiving end of jokes when you're out wearing your vest. I took a cruise to Bermuda years ago and without really realizing it, I was looking a bit military in my shooting vest and brown fatigue shorts. As I was getting off the cruise ship in Hamilton, one of the crew looked at me carefully and in his utterly British dry-humored voice said, "Visiting or invading?" OK, so it was a pretty funny remark, I'll give him that.
But do consider the benefits of owning a vest--I promise that if you buy one and use it when you travel (or just around town), you'll write and thank me later!