Waiting for Samsung Galaxy S3 (GT-I9300) Android Lollipop (L) or 5.0 update. The good news is that you can update your phone to latest Android software, the bad news is that Samsung will not provide an official build. Samsung Galaxy S3 can be updated to latest Android using custom ROM.
Samsung usually updates phones to latest Android cookies up to 18 months. After this Samsung ceases to provide any new updates to the Galaxy devices.
Previously Android 4.4 KitKat build was posted for Galaxy S3 and now the developers managed to port Android Lollipop build for Galaxy S3. The software is quite unstable at the moment, but the developers are working to make it usable.
There are a lot of things which are not working at this time. Here is a list of bugs present in the current software:
Internal & External Storage
Graphics including color calibration and hw composer
Screen off (the device can not enter deep sleep)
WARNING: As lots of features are missing at this moment, this build is just usable of test purpose. If you want a stable software then I will advice you to wait for some more time till the bugs are fixed.
The instructions given in this guide are meant for the international variant of Galaxy S3 with model number I9300 only. Verify device model number by navigating to Settings > About Phone.
Ensure the phone has at at least 80% battery charge to prevent unexpected device shutdown (due to battery drain) while installing the ROM.
Back up data and settings using a recommended custom recovery tool, like ClockworkMod(CWM) or TWRP, as it creates a complete image of the existing phone setup. In Recovery, choose Backup and Restore and tap Backup.
Verify correct USB drivers for the phone are installed on the computer (download Galaxy S3 USB drivers).
Ensure that the device is rooted with CWM recovery installed and its bootloader is unlocked.