Most species in Crawl have the same dietary restrictions (or lack thereof). However, certain races will require different strategies when it comes to getting food.
Carnivorous races include felids, kobolds, and any character who gains ranks in the Carnivore mutation (and ghouls, but they're a special case and have their own section below). Partial carnivores (those who have one or two ranks of the mutation) gain more benefit from eating meat and can eat raw flesh more often, but gain less nutrition from eating any sort of vegetation. Full carnivores (i.e. felids, kobolds, and those rank 3 of the mutation) can eat chunks at any time, but cannot eat any of the various kinds of fruit or bread rations.
Carnivorous characters probably have the fewest problems with hunger, as corpses are by far the most plentiful supply of food in the dungeon. Kobolds have it even easier than most due to their additional saprovore trait, which allows them to tolerate contaminated meat and even eat rotten flesh. If you're playing a carnivorous character, there is no reason for your satiation level to ever fall below Very Full unless you are in an area where edible corpses are hard to find, such as The Crypt or The Abyss. If you wish to explore those areas, be sure to carry some nonperishable rations with you. In general, try to consume corpses and save those meat rations and honeycombs in your stash until you need them in the very late game.
Centaurs are partially herbivorous and spriggans are fully herbivorous; other characters can gain ranks of the Herbivore mutation. Partial herbivores are the inverse of partial carnivores - they gain more nutrition from eating vegetation, but less from eating meat. Full herbivores are completely incapable of eating meat.
Unlike carnivores, herbivores have significant difficulty finding food because vegetation is not a renewable resource. Fruit and bread, while fairly common, are still limited in number and will eventually be completely exhausted. Centaurs aren't too badly off; while they gain less nutrition from meat and have a faster metabolism than average, they can still eat meat. They do have to be wary of eating contaminated meat, as their high metabolism and partial herbivorousness make nausea particularly debilitating; centaurs that suffer from nausea too often will find themselves starving to death in fairly short order.
Spriggans and characters with rank 3 of the mutation, however, lose access to the most plentiful supply of nutrition in the game. Spriggans have a very slow metabolism, which helps quite a bit, but any larger character that gets to rank 3 of the mutation will have a difficult time of things, especially if they also have a faster metabolism. Be sure to carry around extra food if you have an herbivorous character.
Spriggans who know the Fulsome Distillation spell can use it on clean corpses to produce potions of water. With their low metabolism and Fulsome Distillation's easily reducible spell hunger, spriggans can use this to gain nutrition. Each potion only gives you roughly 40 turns worth of nutrition, but in the long run every bit helps.
Saprovorous races are hill orcs, ogres, trolls, kobolds, and ghouls (again, these are a special case), as well as some demonspawn that gain the saprovore mutation as part of their demonic heritage. Saprovores are capable of eating rotten flesh and have less trouble with contaminated meat. This does not give them any further benefits, however; it just reduces the risk of eating certain types of meat and gives them a little more leeway when it comes to finding food.
Troll characters start off with the gourmand intrinsic (as well as Saprovore 2), which allows them to eat meat as if they were a carnivore without sacrificing the ability to eat vegetables. This is an absolute necessity as their incredibly fast metabolism means they basically need to be eating everything in sight. If you're playing a troll, eat chunks whenever possible, expect to need to eat some of your more permanent food supplies on a semi-regular basis, and consider avoiding corpse-free branches entirely.
Ghouls are carnivorous saprovores with a twist; instead of simply tolerating rotten meat, they thrive on it. As they are undead, they cannot starve to death, but their bodies will rot every so often and this process speeds up when they are hungry. They can fix the rot (and heal themselves) by eating meat, particularly if it's rotten. As such, it is generally beneficial for a ghoul character to carry around a bunch of chunks in various stages of decomposition in order to ensure that they always have something to eat when they need it.
Unlike other races, vampires subsist only on blood. At first, they must drink blood from fresh corpses (use e when standing over one), but later they gain the ability to create potions of blood from corpses to save for later. If they go without blood, vampires do not starve (in fact, they gain several helpful resistances) but their ability to regenerate health slows and eventually ceases entirely. So while a vampire doesn't have to worry about starving to death, going without blood still isn't safe. Manipulating blood levels is an intrisic part of a vampire's strategy, so you should plan ahead to determine how thirsty you should be for certain areas.
Mummies do not require and cannot consume food, so they don't have to worry about hunger in the first place.
Casters who have learned the Necromutation spell can use this to get around the issue of hunger by entering a temporary state of undeath. Being in lichform means you require no food whatsoever so long as you maintain it by recasting it every once in a while; it also gives you several nifty bonuses and resistances. There are downsides to this strategy; Necromutation is an extremely difficult spell to cast effectively, you gain the various undead weaknesses in addition to the strengths, and the spell completely removes the ability to eat or drink, rendering potions and foods like royal jelly useless.
Save Your Permafoods
While you will find a variety of nonperishable foods, you should rely on chunks from corpses for nutrition. Save permafoods for branches which contain lots of creatures that are inedible (which may change depending on your species) or that don't leave corpses. Such areas include branches like the Snake Pit and the Spider's Nest, which are both populated by creatures with poisonous meat, or the Crypt and the Slime Pits, which are mostly populated by monsters that leave no corpse at all.
Most of the time, you won't have any difficulty butchering corpses for food -- all edged weapons can be used for this purpose and all characters carry boot knives they can use if they are bare-handed or using a blunt weapon. In some situations, though, a blunt weapon may prevent you from butchering a corpse, whether due to a curse or by having a brand that makes unwielding the weapon dangerous, such as distortion.
Depending on your character, you may be able to get around being stuck with a blunt weapon. Certain mutations will allow you to butcher corpses without resorting to an edged tool; to be more specific, any rank of Claws, rank 3 of Fangs, or the combination of a Beak and Talons can all be used for butchery (though you may need to remove equipment to be able to use your claws or talons). Races that will never need to worry about butchering corpses include ghouls (Claws 1), trolls (Claws 3), felids and vampires (Fangs 3, though vampires can't eat meat), and tengu (Beak and Talons). Others might get lucky with their mutations.
It is also possible to produce chunks from corpses without having to butcher them in a couple of different ways. The Animate Skeleton spell will peel flesh off of bone magically (though this requires a corpse that has an actual skeleton). Alternatively, certain explosive methods of killing enemies will scatter chunks of meat across the room instead of leaving a corpse; such methods include wands of disintegration and the Inner Flame and Orb of Destruction spells, though both have their downsides (wands of disintegration are a decidedly non-renewable resource, Inner Flame may prove fatal if you stand too close, and Orb of Destruction is rather difficult to cast).
Even if you are stuck with a blunt weapon for an extended period of time, being forced to resort to eating permafood is unlikely to prove game-breaking in all but the absolute worst-case scenarios. Often characters end up with more nonperishables than they need by the time they clear the Dungeon.
Dealing With Meat
Most monsters will drop either clean, contaminated, or poisonous meat, some of which may or may not be options for you depending on your character's species. Clean chunks are obviously preferable, but most characters can manage well enough by eating contaminated chunks. Any nausea you contract will generally wear off quickly enough to prevent you from getting too hungry, though characters with fast metabolisms or that rely heavily on spellcasting may drop dangerously close to starving. In emergencies, nauseated characters can still eat when near or at starvation, though this carries the risk of inducing sickness, which may cause further difficulties. Saprovores like kobolds, hill orcs, and ogres have fewer problems with contaminated meat and can even eat rotten flesh in a pinch.
Amulets of the gourmand are extremely helpful in maintaining satiation. Not only do they virtually remove the effects of eating contaminated meat, even for characters without saprovore (though it takes a while for their full effect to kick in), they also allow consumption of chunks while not hungry. With an amulet of the gourmand, you can eat yourself all the way up to Engorged, then switch back to another amulet until you get hungry, then repeat the process.
Eating poisonous meat is a simple matter of finding a source of resist poison. Some races, like nagas, start with rPois, but most others will have to make do with finding some sort of equipment. rPois can be found on rings (though they will not self-identify) or on armour. A potion of resistance will work in a pinch, but using one is generally a waste of resources unless you needed the resistances for something else, like an impending pack of cold-themed enemies. Transmuters can use Ice Form, which grants rPois as well as the ability to butcher corpses bare-handed. Some monsters have meat that is both poisonous and contaminated; while having rPois means you can eat their meat, you may still get nauseous from doing so.
In dire emergencies, you might try polymorphing monsters and hope they turn into something edible. However, this is an absolute last resort, as you are not guaranteed to get something that leaves behind a corpse at all (let alone an edible one). Plus, there's always the chance that you end up facing down something you're not prepared for.
In any case, never eat mutagenic or rot-inducing meat in order to get food; neither type provides any nutrition, and both have side-effects that can prove disastrous. Ghouls can get away with eating rot-inducing meat, but then, ghouls can eat basically any meat without any problems.
Certain monsters will destroy your food supplies or even actively drain your satiation. Giant spore explosions can ruin food items in addition to their other effects, so try to take them down from a distance (not hard, since they only have 1 HP). Packs of harpies in the Shoals have a chance of destroying your food each time they attack, so leave any extra food you're carrying outside the entrance. Some monsters like jellies and necrophages will eat any corpses that they come across, as well as hungry ghosts, which also come with an attack that actively drains your satiation.
In addition to these enemies, other enemies exist that will make corpses unusable for food through the Animate Dead spell. Monsters with Animate Dead include any sort of necromancer, shadow imps, orc high priests, etc.
Experience vs. Hunger
The average player's first instinct is to kill everything they come across in a glorious orgy of bloodshed. However, doing so means that finding things to eat requires exploring farther and farther into the Dungeon while leaving behind floors that are generally devoid of anything edible. You'll have to decide whether you want to kill monsters for experience or save them to eat later. If you are going to leave potential snacks behind, try to spare monsters that don't give much experience, like rats or goblins.
Creatures found in the dungeon's water features are perfect for use as emergency rations. They can't roam around the dungeon so you'll always know where to find them. Be sure to kill them while they're still in shallow water, though; if they flee into deep water before dying, then you won't be able to get at their corpse (unless you're aquatic or a gray draconian). Most fish leave clean corpses, but sharks are contaminated and jellyfish are poisonous - plan accordingly.
Close the Door
Another way to save creatures to eat later is to lock them in a room, though this only works if the creature in question lacks the ability to open doors. This works best if you find a vault somewhere with several low-level natural creatures inside; the various rat/snake or bat rooms that will occasionally appear in the dungeon fit the bill nicely.
It's also possible to lock creatures inside a pre-existing room. The Vaults are a particularly good place for this, as there are plenty of small rooms with doors. This method works best in rooms with two doors, as you can lure a creature into a room, close the first door, then escape through the second door. Having higher movement speed than the creature in question also helps. It is possible to do this in rooms with one door, but a higher movement speed and/or the ability to blink is virtually required.
MAP ........... ..#######.. .@'.....#.. ..#.....#.. ..#.....#.. ..#.....#.. ..#....Y+.. ..#######.. ........... ENDMAP
Be aware that some wandering monsters, such as orcs and goblins, will open doors while wandering around. If they happen upon a room that you've locked something inside, they may inadvertently release it to wander openly around the level.