How can I update my Samsung Galaxy S2 (GT-I9100) from Android 2.3.3 to a newer version? I have a Samsung Galaxy SII (GT-I9100). OS version-2.3.3. Whenever I connect it to Kies, it cannot find an available software upgrade. Is there any other way to upgrade my OS?
Sure, just be aware that doing so you'll lose the warranty! If you want to do it anyway, just go to sammobile.com and look for your phone (just type i9100 in the search box). In the result list, choose your firmware and download it.
To flash it, follow these steps:


Download ODIN v1.85 from here
Unzip the downloaded files, both Odin and the firmware
Power off your phone and boot into Download Mode. To do so, press and hold the Volume Down and Home buttons together, and then tap the Power button until you see the construction Android robot icon with a triangle. Hit the Power button again to confirm entry into Download Mode
Launch ODIN on your computer and connect your phone to it while your phone is still in Download Mode
In case your phone connects successfully, one of the ID:COM boxes will turn yellow with the corresponding COM port number. This process may be time-consuming
Choose the files to be flashed or installed on your phone, which can be found among the extracted files in Step 2
Click the PDA button and choose the file named 'CODE'. Tap the Phone button and choose the file named 'MODEM'. Ignore this step if such file is missing. Hit the CSC button and choose the file named 'CSC'. Ignore this step if such file is absent. Click the PIT button and choose the .pit file. Ignore this step if there is no such file
In ODIN, enable Auto Reboot and F. Reset Time options. In case of the Re-Partition option, check it ONLY if you chose a .pit file in the previous step
Click the Start button in ODIN and the ROM installation process will begin. It may take a few minutes to complete. DON'T DISCONNECT THE PHONE OR IT WILL IRREMEDIABLY BRICKED
Once the ROM is installed, your phone will reboot. When you see the home screen, disconnect the phone from the computer. This may take a LONG LONG time, so don't panic and give it a few minutes


Your Samsung Galaxy S2 I9100 is now successfully updated. Go to Settings > About Phone to verify the firmware version installed.

Enjoy :)