Besides "bricking" your device, most people don't do it because it voids their warranty on their phones/devices. But if you want to remove a lot of the "bloatware" "lagware" from the device to free up more storage space, then rooting is the way to go... if you don't care about your warranty on your device.
Now, here is how to root the S3...
The first process posted by XDA Recognized Contributor mrRobinson works for the AT&T, T-Mobile and Sprint US variants. This method typically does not trip the flash counter, but can take some time. The second method is by XDA Elite Recognized Developer Chainfire. This works for the three aforementioned US variants and the International version. This method is quick, but it does trip the flash counter. Finally, we cover the use of XDA Senior Moderator and Recognized Developer mskip’s toolkit. You can find versions for the four previously mentioned variants of the toolkit. This is a semi-automatic method and does trip the flash counter.
The rest of this can be seen here => How to ROOT Galaxy S3 (all versions)
All the files/apps/drivers etc. that you need are on the website posted. Pay attention and follow the instructions.