One of the nice things about a Leica rangefinder is that the shutter is quiet. This can help when taking photographs on the street since it can minimize the disruption to the scene. I do not have a Leica camera but I do have a Voigtländer Bessa R4A rangefinder. However, the Bessa does not share the same stealthiness as the Leica and the shutter is actually quite loud compared to the Leica.
To demonstrate, here is a short mp3 of the Bessa shutter sound. Since I don't have a Leica, I can't show a direct comparison but the first sound in the clip is the Bessa R4A and it is followed immediately by a Canon 40D so you can hear how it compares to a DSLR. Both cameras were set at 1/125 sec. This isn't exactly a scientific test (I used my iPhone voice memo app to record the sounds) but you can get the overall idea that there isn't a whole lot of difference between the Voigtländer and the Canon.
To hear a Leica shutter, you can find some videos on You Tube.