I might be not as seasoned as you'd like, or own the best equipment as some would think, but I will answer your question.
First, I Don't own a Leica. I am a budget photographer.
It really depends on where I am at. If I want to be stealthy, my EXA black flange with WLF, also I recently converted it into M42, this camera seemed to get away with a lot of things, without people looking at you too pissed off. This I tend to shoot hyperfocal with.
In the winter, I like to have my Olympus 35RC in my jacket. It's small, quick, complete manual override If I need, and a nice lens.
If I feel like there's going to be good stuff, I'll bring my Rolleiflex T with WLF out.
Recently I am doing an experiment, is an F4 with a WLF. Sadly its still too big and scaring people away, I would like to replace my MB21, with an MB 20, so it looks smaller, and less scary. With this camera right now I must use the shoot and keep walking method, don't look back.
That's what I like to do street with, at this moment, I have tired a lot of camera and this set up works the best for me, as of right now. That doesn't mean i won't use other cameras to do street when I have to. Did street with a 650Pro with Power Grip + prism, just smile and nod, and walk away fast, haha.
Previously I also use a Petri 1.9 for street.
By the way, there's also a OM Infinity Stylus in the glove compartment.
You will find a sample of my street photos at http://dehk.wordpress.com/street-photography-best-of/