Is it possible to root my phone without installing a custom ROM? I have a Samsung Galaxy Stellar on Verizon.

Whenever I hear anything about rooting a phone, people always say that you have to install a custom ROM. How do I just use my current stock ROM and root my phone?
Short answer
That very much depends on your device, as the rooting process often is device specific. Following up to the rooting tag wiki will give you some basic info, and also provide a link to our rooting index, which might even already include a link for your device.
TL;DR
Basically, rooting just means to push a binary (su) and a helper app (SuperUser/SuperUser or SuperSU) to the system partition. So as Compro01 wrote in his comment on your question, you're &quot;customizing your ROM&quot; somehow.
On most devices that's all you need, though how that's accomplished is a different thing, as it's a little chicken-and-egg: You want to gain root permissions on your device – and for that, you first have to push those two files to /system, which only can be done with root permissions. So in most cases, this requires some &quot;hacking&quot;, which is what Sparx refers to in his answer might cause your device to be unusable. I rooted several devices already, and when sticking to the instructions the device should not become &quot;unusable&quot; (though I admit there might be rare cases). I had it once a device became instable (apps crashing, device rebooting itself multiple times a day), but that was easily cured by a factory reset.