Downside is it usually voids any warranty and there's always the chance to brick your phone.
^this^
As an example: When I unlocked the bootloader (needed for rooting on most devices) I had to acknowledge that my warranty "may" be voided. I had an issue that was clearly not related to root, but customer service wouldn't give ANY support once they found out about root (citing the click-through acknowledgement on the bootloader unlock). Some places are more tolerant than others though. A different company said there was no problem with rooting and even provided links to stock firmware, but wouldnt address any other type of support. The thing to keep in mind is that once you root, you are kind of "on your own".
I have however unlocked every bootloader on every device possible (around a dozen) and installed custom roms on any that I had the skill to do. Even with all those devices and all that tinkering I have only had 2 bricked devices (and in this case "bricked" means "could not be recovered by any means"). Installing a custom recovery is more useful than rooting. Both can be done separately in most cases but are usually done at the same time for convenience. Custom recovery will allow for making backup images of your rom and a few other handy features like sideloading apps and flashing new roms (not every device will have all the same features).
I think the main advantage to rooting is just to remove bloatware though. Having your app storage full when the manufacturer has "included" a half dozen apps that you never use and cant remove is .....

I would consider root if you have to pass on apps you want because they require root access as well. Backing up your app drawer becomes alot easier once you have root. I just took a look through my own app drawer and didnt see anything that required root except for system monitoring apps and backup apps. YMMV of course
