In the very beginning of the DUNGEON MASTERS GUIDE (page 10) there is an interesting section on the use of miniatures. Since D&D (and later AD&D) evolved from miniature wargames where one figure represented a number of individuals in a formation, some explanation of the scales used needed to be done. HO scale (which is used for some wargaming) is 25 mm. This is representative of 6 scale feet and six feet is the average height of a human male (at least in AD&D fantasy, not so in real life), so Man-size is represented at this scale. Gygax has the following to say on the matter:
The special figures cast for ADVANCED DUNGEON & DRAGONS add color to play and make refereeing far easier. Each player might be required to furnish painted figures representing his or her player character and all henchmen and/or hirelings included in the game session. Such distinctively painted figures enable you to immediately recognize each individual involved. Figures can be placed so as to show their order of march, i.e., which characters are in the lead, which are in the middle, and which are bringing up the rear. Furthermore, players are more readily able to visualize their array and plan actions while seeing the reason for your restrictions on their actions. Monster figures are likewise most helpful, as many things become instantly apparent when a party is arrayed and their monster opponent(s) placed. Furnishing such monsters is probably best undertaken as a joint effort, the whole group contributing towards the purchase of such figurines on a regular basis. Be very careful to purchase castings which are in scale! Out of scale monsters are virtually worthless in many cases. As a rule of thumb, HO scale is 25 mm = 1 actual inch = 6' in scale height or length or breadth.
I have often stated that miniatures add a dimension to the game that is almost necessary to visualize what is happening during combat. It's hard to imagine all the variables going on in combat, and rooms on a map are not just big open spaces - they are usually cluttered with furniture, dead bodies, piles of debris, pools of water, etc. It is much easier for player characters to interact with their environment when the physical aspects don't have to be explained every five minutes. A scale visual representation of a room, cave, corridor, or chamber is also useful to have with those miniatures, as Gygax explains below:
Figure bases are necessarily broad in order to assure that the figures will stand in the proper position and not constantly be falling over. Because of this, it is usually necessary to use a ground scale twice that of the actual scale for HO, and squares of about 1 actual inch per side are suggested. Each ground scale inch can then be used to equal 3-1/3 linear feet, so a 10' wide corridor is 3 actual inches in width and shown as 3 separate squares. This allows depiction of the typical array of three figures abreast, and also enables easy handling of such figures when they are moved. While you may not find it convenient to actually use such figures and floor plans to handle routine dungeon movement, having sheets of squares for encounter area depiction will probably be quite helpful. If you do so, be certain to remember that ground scale differs from figure scale, and when dealing with length, two-man-sized figures per square is quite possible, as the space is actually 6 scale feet with respect to length. This is meaningful when attacking a snake, dragon, etc. if characters are able to attack the creature's body length. With respect to basically bipedal, erect opponents, scale will not be a factor.
So, basically, Gygax is saying that, when dealing with bipedal (humanoid) creatures, you can use 1 square = 3-1/3 feet, so 10' = 3 squares. However, when dealing with a dragon, purple worm, or other long creature, you should revert back to 1 square = 6' scale (or use a bigger miniature to represent its length).
Later editions change the scale to allow for an easier estimation of distance; use of 5-foot squares became common at the end of 2nd edition and were set in stone by 3rd edition. Obviously, this means that we're no longer using HO scale, but some other arbitrary scale. Also, today's miniatures are much larger than those used by 1st edition players. Some of this has to do with the enlargement of the creatures in the MONSTER MANUAL. Giants and dragons were seriously increased in size between the 1st and 2nd editions, and later enlarged again in later editions (sometimes to the point of ridiculousness with some of the dragons).
I've often wondered how a combat would play out using the 3-1/3 foot scale that Gygax suggests. Obviously, it would make figuring ranges a bit more challenging. Then again, using the 1 inch square = 6' scale is just as challenging. All the maps in AD&D were drawn to a scale of 1 square = 10'. It's hard to break that down easily during combat into 6' scale inches. However, if one realizes that dungeon walls were typically 1' thick, and that the space indicated on the map is only floor, then each square by a wall is only really 5' wide (that a character could stand on). However, central floor squares not near a wall are problematic, since they represent 6' of space. Thus, a 30' square room at this scale is 5 squares by 5 squares (instead of being a 25' square room). This could get very confusing. Also, miniatures are made to a scale (with the base) as stated above but there is no way to handle them in 6' scale inches because two miniature bases will not fit in a single square. Gygax obviously pondered this and offered his advice on the subject by exaggerating the ground scale, but again, as he noted, this distorts longer creatures, making them appear larger than they really are.
So how does one do away with the distortion? Obviously, the miniatures are sized to be exactly the length they are according to their description, and scaled so that the humanoid (character) figures and monsters are in the same scale. So, when dealing with this exaggerated scale, one either uses a different size miniature to represent the creature (which may detract from the enjoyment of the combat), or switch to the larger sized squares for that particular combat. In essence, you could revert to the later scale of 1 square = 5 feet and it works just as well (so long as the creature isn't crazy long).
My groups have used other markers to represent battles in the past. My first large group (in which I was a player, not a DM) had a felt board with letters cut out to represent the party, and various shapes to represent monsters. The room shapes were not outlined, but the general area of the battle and positioning of the combatants could readily be determined. We also used graph paper tablets to run combat, with pencil and erasers to indicate positions and movement. This allowed us to represent the rooms, caves, and corridors easily since most maps were also done on graph paper. It also gave the characters a better idea of what the environment was like in a 2-D representation. Ceiling heights are rarely worried about unless dealing with low-ceilings, vertical movement like flight and levitation, or when missile fire is an issue. After all, bows require more of an arc to target distant opponents, while crossbows are more of a direct-line. This is why drow use hand crossbows in their underground realms - these weapons are close-combat, direct-line projectiles. It's hard to find wide-open spaces in the underdark, and even harder to see beyond short range for most missile weapons. Plus, ceiling heights underground vary and may have stalactites that get in the way of bow-shots. During the 2nd edition era, while in college, we used blackboards in empty classrooms to depict battles. These were drawn to rough scale, but again the locations of the combatants could readily be determined, with ranges estimated by descriptions given by the DM.
One of the better ways to represent combat is with a complete diorama-style which indicates all 3 dimensions of the battle field. This is cost restrictive, but the best for visualization. After all, high-level campaigns have flying mounts, spells or magic items that permit flying, and some monsters have flight capability as well (particularly dragons). Representing 3 dimensions also allows for vertical positioning for better shots with missile weapons, determining what happens when someone is knocked off a narrow bridge above the chasm below, etc. Consider Lord of the Rings with the 3-D components of the bridges and stairways in Moria and the orcs crawling up or down the massive columns! Using 3-dimensions makes for a more exciting adventure, but its also more of a headache when using miniatures. Suddenly, you need to track elevation as well as position, and determining distances and angles may not be exact without a ruler or tape measure.
I find that many players use the map grids of today as a crutch. Early gamers would ask their DMs if they were in range, and most DMs would reply "you seem to be, want to try it?" Nowadays the players simply count squares and place spell effects so they end directly in front of their front ranks. Such metagaming has existed in my games as well, but when dealing with a magic-user with an 16+ Intelligence, I let it slide. Such characters are much more intelligent than the common man and should be cut some slack when dealing with spell positioning. After all, they could probably estimate probabilities and calculate ranges faster than the player who is playing them anyways.
I myself no longer cart around boxes of minis, rolled up vinyl maps, or 1' square display pads anymore. I have too much other material that I need to transport. Now I simply create a map using GameTable on my laptop and connect to a monitor via wifi to display the positions of the characters in the game. Sure, I use the 5' squares of later versions, but it's simply easier, and the players don't mind all that much. Is it realistic to say that only two people can be in the front rank in a 10'-wide corridor? I think it is, given that most of those folks are armed with weapons that they have to swing (and probably want to avoid hitting their compatriots) so the extra space is not really "open" during a melee. Three men abreast down a 10' wide corridor is great if they are formed into a military formation, locking shields and using thrusting weapons like spears or polearms). I just don't see many AD&D parties operating like that, especially with a thief checking for traps, or spellcasters using spells or items to detect pits, traps, or secret doors as they go. Some people may argue against this point, but in my groups the 5' space works best.
If you have never played a game with miniatures, I would suggest trying it, just once. It adds a whole new dimension to the experience and really helps the players (and the DM) make the right calls and decisions in the heat of combat! Actual figures are not even necessary. You could use paper chits, game tokens, dice, coins, or anything else. We used to use "M&M" candies in our kid game - when you killed a creature you got to eat the 'm' (which, of course, stood for 'monster'....). If you don't use minis, consider visual aids to help the players make decisions about their environment. If a wizard is going to cast fireball but can't visualize the area of effect, that's a big problem (for the party and likely himself as well)! Of course, if you happen to be a fan of "theater of the mind," and your players can all locate themselves precisely in a virtual mind space, then none of this really matters anyway. It all comes down to how detailed you get with your descriptions and how good your players are at visualizing their surroundings.