For the most part, when I've run dungeons in the past, I've described the corridors solely in terms of dimensions and directions. "The tunnel runs north 50 feet, with a side passage to the left halfway along. Ahead it ends in a T-intersection with another tunnel running east and west."
The problem here is that the choice of which branch to take is a completely blind one, and thus pretty meaningless to the players. There's no reason but sheer whim for them to choose one over another. What they find or the challenges they face afterward are, from their point of view, essentially random, completely disconnected from their choices. Almost needless to say, my players never showed much enthusiasm for the choice. Inevitably they just choose a direction at random. I might just as well have chosen for them, or rolled dice to decide, and it wouldn't have affected their enjoyment, or lack thereof, to any great degree. It's just a pointless procedural step toward more exciting parts of the adventure.
I don't think that's how it's really supposed to be, though. In the Moldvay Basic rules, there's a sample dungeon expedition, a narration of a hypothetical play session. It begins with the party descending through a trap door and down a stair to reach a landing, from which stairs descend east and west. The DM tells the character looking down the east stairs that there's a rank, musty odor coming from below. Based on that information, the party decides to take the west stairs instead. What was the source of that odor? It's never revealed in this sample session, but it enabled the party to make a non-random decision about which way to go, based on their own notions of risk and reward.
I think this kind of observation and information-gathering should be the norm rather than the exception. When the dungeon map presents a choice of which way to go, there usually ought to be some clues available to inform the party's choice. The clues can be either clear, conveying some degree of concrete information to the players, or cryptic, evoking apprehension, fear, hope, excitement, or curiosity, as in the Moldvay example. In other words, it can wholly or partly answer the question of what lies down that passage, or it can present a mystery which can only be solved by exploring in that direction, or it can do a little of both. The point is to give players reasons, or at least potential reasons, why they might wish to explore or avoid a particular path.
This isn't to say that you can't have some nondescript corridors and intersections, but the ones with a few details make for much more interesting choices.
Possible signs a party might find in the passages of a dungeon include:
- Footprints or other tracks (slime trails, drag marks, etc.)
- Corpses or bones of creatures or people
- Smears of blood or slime
- Marks left by previous explorers, such as chalk, charcoal, or scratches in the walls or floor
- Dropped items
- Ordinary non-threatening creatures like rats, insects, or fungi
- Winds or breezes
- Temperature changes
- Dust - if disturbed, indicates recent presence of other creatures, if undisturbed indicates long disuse, at least by corporeal creatures...
- Slopes up or down (possibly very subtle - a chance for the party dwarf to show his non-combat skills)
- Changes in the composition or structure of walls and floor
- Changes in width or height of corridors
- Actual signs or inscriptions, possibly in dead languages or magical script
- Decor or architectural flourishes, such as columns, bas relief carvings, sconces, alcoves, etc.
- Prickling skin, chills, feelings of dread, etc., typically associated with places of magic or supernatural power
Obviously this isn't an exhaustive list, but only the things that came to mind while writing this post. With the exception of things that radiate, like sound, light, and smells, most of these things would need to be keyed in certain locations like traditional "room" encounters. I haven't tried this in an actual dungeon yet, but it seems more convenient to me to list these corridor and intersection features separately from the standard room key. Perhaps they could be noted on the map with letters rather than numbers. In the (probably unlikely) event that you have more than 26 of these locations to note, two-letter codes could be used, e.g. aa, ab, ac, and so on.
Of course, if you give the players these types of clues, you'll need to (most of the time) give them a proper payoff to reward them for choosing to pay attention to the clues. It doesn't necessarily need to be the most obvious or expected thing, but it does need to make sense in a satisfying way. The draft of cold air blowing down one tunnel may turn out to be from a magical bag of wind instead of an exit to the surface. The smell of rotting flesh may lead to a crypt or to a banquet hall, suddenly abandoned for some reason weeks ago, with a once-sumptuous feast of boar and venison moldering on the table. The blast of hot, sulfurous air might come from a red dragon's lair, a portal to the elemental plane of fire, a forge, or a natural volcanic vent. The huge footprints might lead to a den of ogres, or to a goblin lair, where the party finds boots with oversized soles that the goblins use to disguise their presence in the dungeon.
If most of the clues are just there, with no logical connection to anything, players will soon realize that they're of no value whatsoever in deciding where to go in the dungeon. There's also a good chance they may feel cheated the one time that a clue actually is meaningful and could have saved them hardship or earned them rewards. Nobody is going to be pleased with the DM who cried "Wolf!"