Air

If there were a bit less oxygen in the air, we would choke. A bit more, and a single spark could torch all the world's forests (and buildings). We need to breath.

Most life-forms need to breath. Very few would survive vacuum, some don't mind the most poisonous gases. Plants need little oxygen, magical creatures may need none at all.Consider all gases and their interaction with would-be dungeon explorers. Some are indeed poisonous, some irritating, some confuse and limit vision, some make you hallucinate, some are flammable.

To need air means also to need space. Many predators roam around, even if they have enough food. Same is true for birds and other flying creatures like bats. Plants and most insects don't move much, and don't need much space. And don't forget claustrophobia: sentient beings enjoy open places (usually).

If there is not enough food, most creatures move where they expect it. Large creatures often roam across the whole dungeon. They may even open some sections of it, enlarging it for others.

Fire

Fire stands for warmth. Most creatures have a clearly defined temperature range, where they feel comfortable, and other ranges where they feel not. It's good to include at least one extreme somewhere.

What about actual fire in the dungeon? Besides that incinerating pits and lava flows, inhabitants often use fire for defense, warmth and warning. Note fast burning resources and gases, what happens if some part begins to burn, and all the life forms that choke after that fire (little oxygen).

Water

Where there is no water, there is no life it is said. Lesser creatures may survive on vapours, most animals need to drink water. Every day. Forget that cave bear if there is no water around. Include creatures that can draw water out of thin air, out of less lucky creatures, or simply need no water.

On the other hand, the only water source far-and-wide is not a good place for camping: most monsters will sooner or later come around.

Do not forget there can be too much water. Releasing a trap or digging at the wrong place turns your nice comfy dungeon into your grave.

Last note: Not all water is good for drinking

Earth

What is the dungeon made of? Is it actually 'made' or are it mere natural caves? What does prevent it from collapsing? What happens if a cave-in happens, how much (and what) material falls on the unfortunates?

Choose one or more: stone(various kinds), bricks(various materials), limestone, earth,...
Choose again: digged/tunneled, built and buried, natural caves, adapted,...

Earth means base, the fundament things stand on. What would an earthquake do to your dungeon? And those adventurer-freaks, digging their way somewhere?

In a way, food is a base for all living beings, in whatever form it comes. Earth itself is food for plants. Tunnels hewn into rock are seldom over-grown, earthy caverns would be.

Food

This is a parallel category to water. There needs to be food for these creatures, insects, and plants to be able to survive. Now plants will be food for insects and small animals, while the food chain increases larger animals eat the small plant eaters and so on.

However, in an environment such as a dungeon or cave where there is no light source, very unusual and sturdy plants will be the only few to survive in the dark depths. Will all of these plants be edible for a normal human or non-cave/ dungen dwelling denzien? Probably not. Care must be taken on what food source is gathered in the depths. It could be your alst meal for many reasons. Poison is most common, while it may not kill you outright it may hinder you long enough for another predator to come along and feast. Possibly the result of your death revitalizes the soil bringing nutrients for more plants, drawing more animals for the hunter.

Also to add on that, where there is a food source for one animal, another larger animal will be close by. Before stopping and marveling at the seemingly clear river flow, or the large patch of mushroom stalks standing three feet high, remember something probably uses this underground oasis as a hunting ground.