I have often been asked the question if Android devices can be jailbroken like an Apple device running IOS. The answer is a definite yes. This is a legal process, and it is called rooting.
This tutorial to Jailbreak Samsung Galaxy s3 suggests an easier process than jailbreaking IOS devices where the latter needs a little understanding in the complications of such things like backing up your SHS blobs using tinyumbrella. There is also currently no need to worry about updating baseband like you should be careful not to do in Apple iOS devices.
This other site contains other tutorials on how to jailbreak other Android devices on phones like Samsung Galaxy S3, Note, Note2, Mini, Motorola, HTC, LG, Xperia, among others.
Before rooting, you should understand the two main risks.
1) rooting can void your phone’s factory and/or service provider warranty in many cases. However, most rooting applications and methods can be easily reverted.
2) if the rooting process is not completed correctly it could damage the software. This would require a factory recover, causing all data on the phone (contacts, apps, media) to be lost, or it may even render your device useless, to the point where it can’t be saved unless examined by a technician. However, if you are just even slightly computer adept and able to follow the instructions for the rooting method you use carefully, you shouldn’t have a problem. Make sure your phone’s data is backed up before attempting any rooting.