Well, the above two posts put the best advantage to rooting quite succinctly. To go into more detail though, rooting basically enables full access to all files in your handset's internal memory. That full access lets you install custom ROMs such as newer versions of Android or ones that are more suitable for better performance and battery life. It also lets you install root only apps that can do more than some normal apps, such as Wi-Fi tethering.
Essentially, we root our handsets to gain more control over what they can do and how they do it. We are able to tweak how things work and what is installed to perfectly fit our own expectations of the handset itself. Given the proper research and understanding of what you are getting into, and support from these forums, you can be rooted and enjoying a newer, more svelte version Android in under thirty minutes. It really is worth the effort to root and gain that extra control.