By running custom ROM's, you get the opportunity to have a different UI to the one that came with your phone. My Desire HD shipped with HTC's stock "Sense" overlay which is liked by many, but I wasn't overly impressed with it.
I opted for CyanogenMod7, which is Vanilla Android, but it is possible to get ROM's that are from other manufacturers if you like - by this I mean that it may be possible for me to run a Samsung based (sorry... don't know what Samsung call their UI) ROM that has been ported to the DHD.
Some custom ROM's have custom kernels in them and, as such, allow for under/overclocking of the CPU (to give the processor more or less power, depending on what you are doing) or even undervolting (to supply less power and hence increase battery life).
I am about to install a custom ROM that is based on the newest version of Android (Ice Cream Sandwich), which may not even be coming to the Desire HD... this is a good enough reason to me to root and install custom ROM's.
I do not know if there are currently any ICS ROM's out there for your phone (I am sure that another member will be able to clarify), I have just mentioned it, as it is another benefit of a custom ROM.
EDIT - thread moved to All Things Root section, as you will get better answers from other root users.