Up until playing 3E I have never really used a battlemat, or other easily-manipulable representation of combat. The most the groups I was involved in bothered with were scrappy diagrams quickly sketched on a sheet of A4, with arrows and rubbings-out as combat progressed. Not ever having done anything else, I was happy enough with this.
Then I played a few games using counters and a homemade battlegrid. Whoa! What a difference it made! To be able to actually use the movement rules that most games include, and take real advantage of ranges and areas of effect was an eye-opener. Suddenly many more real choices opened up for characters (and the NPCs). Rather than arbitrary DM-determination of the value of actions, everyone could see what the effects of a choice were. Now I could see that I could run up to the door and drop a fireball into the midst of the badguys, rather than the DM going "err... probably too far away to do it this round, but you'll be in place for next round."
To some people this seems like it interferes with the ability of the DM to set a scene and manage it. But I rather see that it makes the DM take into account the game rules and abilities which represent the capabilities of the PCs in the physical sphere. It doesn't stop me role-playing my character; I still choose how, when and where to fight based on the PC's personality, but now I can also add in a real judgement of the PC's game-described abilities, rather than relying on the DM's guesses. In combat especially, the DM has a great deal to do; it's no wonder that when pressured they tend to underestimate the capabilities of the PCs (that he's not actually playing), and overestimate (or precisely know) the abilties of the NPCs that he has the details of in his head, or before him. It's not a matter of the DM being 'unfair', but an unconscious bias arising as a fairly inevitable consequence of him being the only person who really knows what's going on. I think Zappo put it best when he said that it's a game of shared imagination. Using a more detailed representation requires the DM to share more of his 'omniscient' perspective.
So now I always try to get some sort of battlemat used in all the games I play. Not all GMs are willing to do so, and as a consequence combat sequences in those games are always far more fraught and stressful, as I struggle to get the GM to actually describe in game terms what the situation my PC perceives is. And I notice that the players with the stronger and more forceful personalities leverage that surety into more advantageous combat situations ("but surely if he can see me, I must be able to get a bead on him!").
So, no, I really love the battlemats, and the sense of shared activity and community it helps create.