I've rooted for a lot of reasons. Tethering is one, as US carriers like to lock you out of that function unless you pay them extra. Other reasons I have rooted phones have been to do things to boost performance and improve my battery life. Also to remove "bloatware," software that the OEMs and carriers put on the phone that you may not want, or that take up space you want, and may run in the background and chew up battery or use data. These are non-erasable because they are installed as system apps, not user apps, but rooting allows you to remove themI then used custom ROMs to get me onto the latest version of Android once the OEM updates stopped.
But Android has come a long way. This phone has fantastic performance and battery life right out of the box. Rooting to improve that isn't really going to make the kind of difference it used to. You can disable much of the bloatware in settings (still can't remove it though). Lots of people flash custom ROMs because they don't really care for the OEM's user interface, but I actually think this one's quite good.
I personally can't imagine being on a non-rooted phone now. Even if I don't really need it to change a lot, I still like to know that I have full administrative power over my phone. And with root, you can use apps like Titanium Backup to backup all of your apps and data. If you flash a recovery, you can use it to make full-system backups. For me, this alone is worth rooting for. I also feel more secure with it, as should something go wrong, I have access to the full arsenal of tools available to correct it.
Your mileage with root will vary. It all just depends on what you seek to do with it. It's generally a safe bet to assume rooting will void your warranty. You can un-root or flash the whole phone back to stock though. I consider root a necessity for myself, but the majority of people run their stock, non-rooted phones everyday just fine. It all just depends on what you want to do with it.
If I were you, I would plug the sim card in and just try using the stock, unrooted phone for a bit. Especially since it's your first Android device. See how you like to use the phone. See what you like, and what you don't, and if there's something you want to change. If you want to change a lot of things that require root do so, then consider rooting it. If not, just enjoy using what is currently the bleeding edge of the Android market. Seriously, this device is FAST and will provide a great user experience with or without root.
Cheers, and congrats on your new phone!
