Hey Larry. Congrats on your new 'one'. an absolutely brilliant device. I'm enjoying mine tremendously. As far as your question on rooting goes, there are many advantages to rooting your android devices. One of the main ones being the ability to install custom roms, and thereby bringinging the customization and performance capabilities to a whole new level. before I purchased my one, I had rooted my galaxy s3 and swore then that I would never have an android phone again that wasn't rooted. Just too many advantages to a rooted (super user access) device. I decided to install cyanogen mod (then 9) on the gs3 and never looked back. There are many outstanding roms with various UI's to choose from, but I found CM to give me a great balance of a more 'stock' android look with a flair of its own. As well as being, possibly, the most popular custom ROM of all. As of yet, I have NOT rooted my HTC One. I have the AT&T variant, and before rooting it's necessary to unlock the bootloader. Now as far as the gs3 goes, the bootloader came already unlocked, and there were many incredibly simple root methods available on the web. and considering I'm not the most tech-savvy person in the world, I needed an idiot-proof method. As far as the one goes, and considering the bootloader issue, I have yet to find a 'simple' (to me) root method for it, that doesnt require typing command lines, and such. And the HTC one seems to rate, overall, as a 'medium' difficulty level on the hackability scale (according to Android magazine). But they WILL come, and I'll definitely have my 'one' rooted. There are some great root apps available in google play.
As far as anything 'bad' happening, there's always a risk involved, for the tech 'non-savvy', to attempt rooting. Your device, worst case scenario, could be rendered practically inoperable. But in all honesty, if you can follow instructions properly, and have at least some basic technical knowledge, with the information available on the web (in particular by such established geniuses as XDA developers), the likelyhood of such a disaster happening is very remote. And, as I say, the things you can do with a rooted device are incredible.
So Im probably going to wait a while before attempting to root mine. But it's defenitely gonna happen.
OH, and btw, AT&T doesnt look too kindly to having their phones rooted. At the very least, it voids the warranty on the device. and Also, If you ever want to trade-in your device, at the carrier retail store, to get credit towards a new phone on an upgrade, if you still have the phone rooted, they may not let you trade it. An option being that you could certainly un-root it.