Innumerable reasons. Since your posting in the Verizon thread I'm gonna make a huge leap and assume you have a Verizon Galaxy S3. Let me just start by saying that Verizon thinks they are more special than every other carrier. They add more b/s bloat apps, they are the slowest to update, and they "lock" their software down more than most. This phone is more loaded with b/s than any other phone I've had. If you want to be able to remove that stuff you have to root. Also, as I said above we are always last to recieve our updates. Sprint just got their premium suite update with multi-window, project butter and the rest of the sweet stock firmware upgrades. I guarantee you that every other U.S. Carrier will get theirs before us as well. By the time us Verizon GS3 users get our "official" premium suite, the next version of Android will probably be out. Be it 4.3 or 5.0 key lime.
Once you root and install custom recovery, you have the ability to choose what software you do or don't want. There is literally hundreds of developers out there who are constantly developing new software and new features to add to your phone. And best of all... It's all FREE (though if your a good little Rom flasher, you will donate to them). All you have to do is go and download whatever custom rom your interested in, put it on your Sd card and install it from your custom recovery. Almost every developer makes their Roms in zip format so all you have to do is put the rom on your phone and basically click install. You rarely have to use your desktop computer to install anything (though you will probably have to use it to achieve root in the first place). If you were smart though you would learn as much as you can about using Odin and adb as you can.
In short, rooting enables you the end user to actually unlock the potential that your device has, instead of being stuck with whatever your Carrier/Samsung decides you get.
I know it all sounds intimidating when reading about it, but it's really alot easier than it sounds. Just do as much research as you can and read read read. If you are serious about this, then I would recommend this root method for the Verizon Galaxy S3.
[GUIDE] Root for Jelly Bean 4.1.1 or 4.1.2 OTA ***UPDATED 3/5*** - xda-developers
That's what I used and it is pretty straight forward. Though it will require you to have a windows computer. XDA is the site to go to (no offense Android Central, I love you!!) There you can find just about any information you need regarding your phone and rooting.
Good luck!