These aren't specific to me, but here are the top 15 reasons to root....in no particular order.
1- Ability to back up and save anything and everything. As xmr405o said, normally there are some things that can't be backed up, but after rooting you can even back up and restore you home screen layout, the entire content of the OS or a specific game you don't want to lose that high score on.
2- Custom ROMs. Once rooted and with the proper developer support there are a bunch of different custom ROMs out there for devices. These range from simple adjustments to the software all the way to fully tricked out versions of the OS. Some developers have gone as far as offering HTC Sense to Samsung phones or stock Android to phones with custom UIs. It is another way to make the phone your own.
3- Mods. Not like me
, but modifications to the phone that allow for different added function or customization. Changing the battery icon, custom fonts or removing the clock from the status bar are a few of the more popular options.
4- Remove bloatware apps that the carrier forces onto the phone. These could just be games or free trials, but if you don't want them there you can remove them.
5- Wifi/ Bluetooth Tether. Just about every phone is capable of doing it, but some are prevented by software. Rooted wifi/bluetooth tether apps offer the ability to do what the phone is capable of. (Not saying I agree with it and in many cases it does violate the carriers TOS, but it is there)
6- Remove ads in apps. There are apps out there like AdFree that work just like an Ad Blocker in your browser.
7- Updates beyond the EOL for the phone. As with custom ROMs the developer community for a specific phone can extend the life of the phone beyond what the carrier or manufacturer is willing to do. There are plenty of phones already running ICS even though only a few have it officially.
8- Custom Kernels. Just like custom ROMs these can ad performance or save battery life.
9- Overclocking and Underclocking. Just like custom kernels these can improve the performance of a phone or conserve battery life depending on your goal.
10- Root only apps. There are a bunch of apps in the market (play store) that require a rooted device to function.
11- Stop Carrier IQ. Most everyone knows what it is now, but can't stop it unless they root.
12- Apps from other OS versions. Some of the custom UIs do have cool features, but they can't always be installed on just any device.
13- Google Nav outside the US. If you want it and aren't in the US you have to root for it.
14- New/old functions on older phones. With some phones/Versions of Android it is the way to get Apps2SD and screenshot functionality.
15- Because it is your phone and you can.
Android is all about freedom and the ability to root your phone and take total control of it is one of the most sought after features.