B most of the time, L sometimes if I'm playing one handed, although it's harder to control that way. The R button on my 3DS doesn't work reliably so that's not really an option haha.
Wow! I'm surprised to see how many people prefer to use the B button... I always felt R was the most comfortable - so that's what I typically use to run. ...Not that I get to run often. (Stupid grass. ಠ_ಠ)
It definitely helps me when playing that mini-game where you have to run around and smack the acorn-robot-thing, though. The B button is so close to the A button that it makes running+smacking awkward... So yeah, R BUTTON ALL THE WAY.
B for running! I use R to speed up text. I used to use B for that as well, but that sometimes caused me to accidentally refuse villager's requests when skipping through the text too fast... My villagers have been liking me lots more since I've been using R.
If I'm just running somewhere (museum or re-tail...) and do something else with my right hand, L. Usually it's R but sometimes B.. R messed up a lot of bug catching for me since I keep messing with both L and R constantly while running or doing things (meaning, I take a lot of screenshots by mistake and none when I realize I should have)