Permanent back-buttoner here.
Pros:
It's basically manual focus without the faff. I no longer have to switch between auto and manual focus. Shooting in the dark means I can't use autofocus easily. Nothing worse than getting the shot all lined up and then you press the shutter only for the AF to start hunting about to no avail. It's also handy when doing focus/recompose in daylight.
No focus delays because shutter and focus are no longer linked. I have control over both directly and independently.
I can also leave AF in tracking/servo mode so I can quickly switch from static focus to tracking focus without messing about in menus.
Cons:
If you hand your camera over to someone to take a shot with you in it, you need to either switch it back or accept lots of blurry shots of you.
Post edited at 13:56