Well, I suppose this goes here if you allow "PnP" to be a console. I can't think of a better place to put it.
I'm not fond of grids. I feel they are unnecessary. Having a definite position sort of ruins the feel of free imagination.
Grids do help with communication. I know frequently its there is question of who is where. This eliminates the problem. However, while it can be chaotic, the game still progresses and the four DMs I've played with have all handled the chaos well. What is important is "Clare is behind a tree writing in her book" (Clare Sulristar is probably my favorite character that I created). As long as everyone knows if she is in range of whatever is important at the time, does it matter exactly which square she is in. Perhaps that not the greatest example since all Clare really does is watch from a distance (she's an RP character, although she is excellent in combat). Another Character of mine, a Duskblade, had a whip. It was important to know if she moved would she still be in range of her target and outside the range of all hostiles. Simply talking to the DM ensured I never had any problems. In another instance, in the campaign I'm currently playing in (a Star Wars D20 campaign) Lloyd is a sniper. I needed to find a place for him to set up his bipod, trying to avoid falling prone. A simple grid would not have helped. When explaining where I was in respects to a particular door the GM had it all in grid form in his head and explained how Lloyd would be situated.
Placing these characters in a rigid grid would draw me out of the illusionary would I was trying to created. For me, D&D, or equivalent, is not about the combat or the rules, but about the world. That also happens to be why I tend to push things to their limit (making Clare, for instanced, required that all her gear be made from scratch, I had to legally make an entire race, and then clean up the left over problems resulting in over 80 pages of documentation). I don't care if I push the rules of the game as far as possible, I care about the world the character lives in. If you tried to write a series of books explaining how the real world worked, you would find that you will fail. If you consider the imaginary worlds to be a world of their own, why would you try to adhere to a finite set of rules and pregenerated crap? Similarly why would you restrict the locations of your characters when in the real world such limitations aren't observable (its arguable whether or not they exist, but thats for a different topic). "Lloyd takes a 2 meter step" verses "Lloyd steps to the side". Would Lloyd take a 2 meter step, or would he simply step to the side within the world of Star Wars? When you step to the side, do you measure out one unit, whatever that may be, or do you simply do it?
In general I'm a strong believer in the world over the game. Using a grid lessens the worlds importance and so long as the DM or GM is competent, it should be necessary.
[edit] Oh, I have never been DM before by the way.
[edit2] I change the title of the poll a bit since it didn't seem to alter the way people would have voted. In the discuttion itself please feel free to discuss anything on the subject. Miniatures were left out of my opening post, and aren't allowed to influence the pool, but they also may be mentioned.
[edit3] When talking about miniatures make sure its about their use as representations, now about how bad ass they look or likely to have them for reasons other than as a proxy for your character.