Tough question. We’re talking about Android, by the way. I’ll start with a case against rooting: Well, first off, what is rooting? If you asked yourself that question before I threw it at you just there, I’d advise against rooting, unless you are looking for a hobby more than you are looking for a phone. Root is the superuser account on Linux, UNIX and UNIX-derivatives. Lets you modify and execute any file however you want basically, regardless of the permissions set on the filesystem and bind to any network port. And Android is Linux, more or less, the Linux mascot is a penguin (pic related); so there you go, rooting.
Your Android phone was badass the moment you hit the power button the first time. There’s a ton of software on the market, a lot of which is both good and free (and some good ones that cost a buck or two). If you come across an application not on the market for some reason, you don’t need root to install it, usually. Good chance you won’t feel the urge to root unless it’s an old habit from your WinMo days (well, that was called hardspl, not rooting, but similar idea).
On the other hand, there are some things that might tip the scale of your decision to root over the edge. Some examples include wifi tethering, manipulating the trackball or LED or your phone’s equivalent to give you differently-colored notifications depending on the notification, going crazy with skinning, VPNing, screen capturing, remote wiping, making backup images, tweaking the YouTube client to use HQ by default and adblocking. Among other things. Maybe the biggest reason is plain old curiosity, the type that brought you to this article in the first place.
