Ever since I first cracked open a copy of The Hobbit and The Book of Three (probably my two first real forays into fantasy fiction) I've been impressed with the power of a good map to deliver an important part of the experience. I used to spend hours looking over the large, fold-out map that came with my first copy (now lost, sadly) of Unfinished Tales, and wondering what those other, obscure places that Tolkien never really mentions in the narrative were like. Sea of Rhûn? Huh? Khand? What kind of place is that? Minhiriath? Tharbad? Cardolan?
When I started drawing my own maps in junior high, I followed a somewhat isometric, stylized version of map-making, inherited and inspired by Christopher Tolkien's masterful map, I'm sure. Most fantasy novels that include maps do, it seems. And I used to draw them all the time. I drew dozens, if not hundreds, of maps. That's how I doodled during class. I didn't do anything with most of them; simply making the map itself was the fun part of the exercise. I started roleplaying games in a time when most everyone was playing D&D (I didn't really start until the Basic box in 1983 or so, but I think my very first session may have been a lingering OD&D game. It didn't click for me at the time) and playing D&D back then quite often meant "homebrewing." This was before any significant or serious attempt had ever been made to present a coherent setting for anyone to use, so it was expected that GM's would do most of that work themselves.
I've since had second thoughts about the advisability of starting the job of GMing by drawing a map. I'm a fan of the Ray Winninger methodology, the gist of which is: don't create more than you have to, or you'll risk burning out. He advises only mapping a very small local area to start with. I've even run games with no map whatsoever before, and that's certainly doable. The methodology makes some sense; if you're going to be playing in the geographical equivalent of the British Isles, do you need to be mapping the geographical equivalent of the Ottoman Empire?
However, I think that---to a certain point---maps are a useful and fun artifact in their own right. I've found that making maps really helps to stimulate adventure ideas, and even campaign ideas. There's nothing quite like the implicit mystery of mapmaking: what does that name over there mean? What are people like over there; what kinds of interesting things are happening over there, etc.?
Game designers will tell you that the desire to explore is a compelling motivator for many gamers, and I believe it. I personally love that aspect of gaming myself, and nothing motivates me to explore more than a good map.
That said; I'm in the middle of a couple of mapping projects right now, for my "modular fantasy campaign setting elements" wiki. I've got a very sketchy one for my hobgoblin empire already posted (but I'll want to do a "prettier" and possibly slightly more detailed one in the future), and I'm turning my attention soon to the concept of a "vampire kingdom"... one of the first things I'll need to do for that is, of course, draw the map.