The Grid

Do I use Minis or Not?
The original White Box edition of the world's most popular role-playing game is an extension of miniature wargaming, even though the booklets say the use of miniatures are optional. Having a mix of medieval miniatures in my collection prior to discovering the then new game, we occasionally used them to show marching order or combat positioning (with dice filling in for monsters).
The reality is that the use of miniature figures in role-playing has some advantages and some limitations. Most RPG systems I play with do not rely on a tactical display or "grid" to adjudicate combat. There are exceptions, however. The Fantasy Trip - recently republished by Steve Jackson Games - uses a hex based display and both 4e and Pathfinder heavily favor the use of a combat display gridded off with 1 inch squares. Such grid-based rule systems make the positioning and tactical movement (flanking, etc.) of miniatures a significant part of gameplay.
A "theater of the mind" play style where there is no physical representation of the in-game character combat action, but rather where everything is done through verbal narrative itself has other advantages and disadvantages. When players are forced to use their imagination rather than look at a display, to imagine what the action looks like by drawing on memories and the referee's verbal description, there may be a slightly different "picture" in each player's mind, but the potential is there for a much more vivid mental image to form than any group of miniatures and model terrain can supply. It can be a bit difficult in a melee to picture just where each combatant is at in relation to others using theater of the mind, but I find that the use of imaginary terrain features and relative areas such as, "My character is standing by the big tree in the middle." can be helpful.
Theater of the mind is especially useful in creating a sense of horror at the table. It is an old adage in the film industry that the monster ceases to be scary as soon as it is seen clearly. What our mind imagines is often much more creepy than any picture held up before the players or any painted game figurine. In the dark (recesses of our mind) anything can exist.
The clever referee may alternate deliberately between the use of both techniques, miniatures and theater of the mind, depending upon the desired effect (or available resources). Even games that are built around the use of miniatures and a combat display can, with a little thought and cooperation from players, be run as theater of the mind. Obviously, placing a few miniatures on a map will not adversely effect a game that assumes no miniatures will be used. A friend, at whose table I am a frequent player, makes good use of his collection of detailed dungeon terrain and miniatures and I definitely see how their use can shape play in a way not possible without them. I have used various grids and miniatures in my own games, but tend to rely on verbal descriptors and mental images more in my personal refereeing. Part of that practice is my preference for an in-game mood I call "dungeon horror".