Like many here I don't tend to rush through games. However I'm more likely to explore tha map of a game if there was a fun way to explpre the map. Such as driving around aimlessly in GTA or using Epona in Zelda, or web-slinging in Spiderman.
I wouldn't want to run everywhere on foot, which is why I tend to use fast travel most of the time on Oblivion (the horse controls and animation are very bad).
Take a game like Shadow of the Colossus, the horse and character animation and programming are exceptional, and very fun to take advantage of. You can look around the plains and even though the whole world there is very empty for the most part, the long view you get of the Temple, the Bridge and various other easter eggs or landmarks are incredible to whitness on your journey to the next colossi.
Then take WindWaker, fun game, interesting style, one in a long run of exceptional games. But look at the travelling scheme. You're on a boat in the water, and the only thing you tend to see are sillhouettes (sp) of islands on the horizon, the odd seagul, other than that it's nothing. I usually find myself throwing the boomerang behind me and sail away from it just to keep myself preoccupied.
Ofcourse if you find something like an enemy boat or tornado on the ocean (but that's not likely to happen) then it still gives you something to do or look at rather than a looping sail-cycle. Please note that I'm just criticising the travelling, the action in Zelda WW is incredibly fun to play.
So yeah, to sum up this whole post in a nutshell (and pretty much nulling the reason why the post should be long to begin with), I'll explore a game's map and side quests if the means of getting to those locations is fun and far from mundane.
Edit: I'll also be doing what DeityLink said, and will be avoiding the forums from Nov19th - Dec 7th... Use that time to talk about me behind my back in the open. :3