The advantage of focusing through the taking lens is that unlike rangefinders this method works with telephoto lenses. It's very hard to use a rangefinder accurately with anything much more than 135mm (and even that's not easy.) Similarly with macro or close up shots. However, rangefinders have many advantages, the viewing image is never blacked out like a SLR does when you click the shutter, also you can see around the periphery of the area covered by the lens, seeing objects moving into the frame, also the two main advantages are that since there's no mirror the camera can be used at slower shutter speeds without getting moved around by the mirror slapping against its stoppers, and again because there's no mirror needed the back element of the lens can be very close to the focal plane (where the film or sensor is), this means smaller lenses can do the same job as much larger ones on an SLR - they are also sharper because of this, and suffer less distortion.
I use a Leica M6 for many of these reasons, it's a beautiful rangefinder camera. http://en.wikipedia.org/wiki/Leica_M6