I'm not sure I agree 100% with Mike on this one. His observations about game design and power/control issues are very valid, but I'm not sure that avoiding miniatures necessarily pulls power away from the players. In a way, using miniatures can take power out of the hands of both the players and the DM putting it in the hands of the game system itself.
Let me illustrate by an example from my most recent session. In an encounter, one character was far away (in a very large room) fighting orcs while the rest of the group was contending with other concerns--it was a complicated encounter. The character fell under the onslaught of her enemies. If I hadn't been using miniatures, I'm sure I would have just said, the next round, "the orcs Jenna was fighting run over to where the rest of you are." But instead, we were using miniatures. It was obvious to everyone around the table, because of the miniatures, that the fallen character was surrounded by orcs who had nothing to do other than use coup de grace. (And they did.)
The power, in that situation, was taken out of my hands and lout the players' hands. It was in the game's hands. On some level, none of us wanted to see Jenna get killed in that way, but because the miniatures and the rules made it so clear what should happen, we all knew that if it didn't happen, we'd be reducing the verisimilitude of the campaign. (This was not verbalized in any way, but I'm sure it what was going through everyone's mind.)
The game is there to provide a neutral basis for reality, and the DM is there to both arbitrate and shape that reality. The players are there to, in a way, arbitrate and shape the reality for their individual character. The more clearly you define things--which is what miniatures do--the more power you put in the hands of the game itself.
In other words, if you're running a narrative encounter (to use Mouseferatu's term) as opposed to a miniatures encounter, no matter how careful and exacting you are, both DM and players have more imaginative "wiggle room." In the end, I think this probably works equally in the "favor" of both NPCs and PCs, though--both DM and players.
I also think the advantage of using miniatures as a visual aid and an elegant feature of the game outweighs this concern, but I think it is a concern.
I also agree with Mike that "miniatures take away from roleplaying" is a bit of a cop out. Use the miniatures to show where your character is in the middle of a tactical encounter, and then ignore them for the rest of the session. Surely having miniatures doesn't really affect how the PCs negotiate with the bullywug king or how they all interact to decide whether enter the wizard's tower through the door or the window (for example). I think the real issue is that people who use miniatures in their games are assumed to be running hack-n-slash only games, where combat is the only thing that happens, and thus no real roleplaying. That certainly doesn't have to be the case. Post hoc, ergo propter hoc. The DM and the players control how combat heavy the campaign is, not the miniatures.
For the curious, Jenna was an NPC, but a much beloved companion to the PCs.
And yes, I use miniatures in probably about 95% of my combat encounters. I love them. But I can see good reasons why others don't want to use them. That they prevent good roleplaying is not one of them, though. I do think the game should cater to miniatures avoiders as much as to those of us who like them.