If you are having battery life issues then check out the best sources of information and study up on issues like wakelocks, runaway apps and other cool stuff. For general android issues
http://forum.xda-developers.com/index.php
For Samsung SIII owners specifically try
http://forum.xda-developers.com/forumdisplay.php?f=1563
For those too lazy to study up my quick advice is:
1. Get a good app like GSAM battery monitor to identify the apps that are chewing through your battery, which over time are often ones you aren't even using.
2. Uninstall anything you don't use.
3. Limit notifications and syncing for those apps you don't need constant updates - Facebook, whatsapp, google maps and skype are notorious battery killers with wakelock issues.
4. Optimize your phone specific settings. If you don't use/like/need it then disable it. E.g., NFC, S Voice, S beam, misc. accounts, haptic feedback, smart stay, touch key light greater than 1.5 seconds, location services, etc.
5. If you are moderately adventurous consider rooting your phone then installing proven apps like titanium to remove bloatware and implement additional optimizations.
Has a very low risk of screwing up your phone if you follow the advice in xda-developers for your specific phone. Yes it does technically break the warranty but very easy to un-root back to the factory settings.
6. If you are very adventurous and like playing around with your phone's OS and comfortable with the potential consequences then consider flashing your rom and trying mods like CyanongenMod 10.
Note: this has a moderate to high risk of screwing up your phone if you don't know what you are doing or don't strictly follow the advice of the experts.
7. Brute force - simply buy a huge battery and custom case for extended batteries.
http://forum.xda-developers.com/showthread.php?t=1843896
Other useful links and ideas:
http://webcazine.com/1430/how-to-improve-battery-life-of-samsung-galaxy-s3/
http://forum.xda-developers.com/showthread.php?t=1379778