I rarely, if ever turn my phone off. but I do a reboot about every 2nd or 3rd day and it seems to run like a dream. I haven't noticed any problems or gains from not turning it off.
I just got my S3 last Saturday so haven't even had it a week. My old phone, the S2, was such a refurbished piece of crap that I literally had to restart it every day. I had to complain to Sprint, I can't even tell you how many times, to be able to upgrade early. So far still ridiculously in love. Anyway, I only ever turned my phone off when I restarted it. Can't get over how fast the battery recharges on this phone. Super fast.