I joined this forum specifically to comment on this issue.
my S3 used to be great and the phone used to last near enough 2 days and I started having battery drain issues a couple of weeks ago. I assumed it was something to do with the fact that I had dropped it in the bath (phone still worked fine btw) !!
However, my battery usage went from two days to about 1 day. After reading various threads I did two things to my phone yesterday:
1) Set background sync to "Never" in K9 mail under Settings -> Network -> Background Sync.
2) I disabled some services on my phone as described on the following thread. forums.androidcentral.com/verizon-galaxy-s-iii/202816-safe-disbable.html]Safe to Disbable - Android Forums at AndroidCentral.com
From a full charge yesterday evening my phone is now at 77% charge after 12.5 hours with a few phone calls and checking texts etc, but not a huge amount of use. So 23% battery used seems to be a big improvement.
I'm going to keep monitoring the phone to see how it goes but for now I see a definite improvement.