Use a rangefinder with a 50 or 35; especially a black Leica M. It is diminutive, quiet, unassuming and often people do not respond to it in the same way as an SLR with a large lens. A rangefinder is much less recognizable and certainly not as potentially threatening as a big F5 or D700 with 17-55 2.8 mounted. A big professional SLR is INSTANTLY recognizable by most people and looks somewhat more like a CANNON than a camera.
With the right camera and some practice, you can learn to set and pre-focus for an interesting scene or face developing up ahead that you want to catch. It is possible to make one or two exposures very quickly and quietly in this way and when I'm out shooting street, it's very seldom anyone even notices that I just took their photo. If they do, I don't pay any attention to dirty looks. I am always moving along when I'm shooting and if there's any eye contact after the photo, I just give a little smile and a thank-you nod and keep moving. I have never had anyone pursue or yell about it.
I don't think Bruce Gilden's brash and brazen way - if you watched the YouTube video - would fit for most people's style of photography, but I can only speak for myself on that point. Street photography is about being discreet, quiet and going unnoticed by the people you are interested in. Unthreatening body language and movements have as much to do with that as the type of camera you use, but I still think a rangefinder is more suited to street than an SLR.