On Fantastic Beasts

I've frequently encountered problems with the use of real-world animals in D&D. 

Like other "monsters", animals might appear in dungeons or in the wilderness. Many animals don't seem to belong in a dungeon - there might be a pack of giant rats, a nest of spiders, or a poisonous snake in a toilet for some reason, but there probably won't be a herd of deer on level 3. 

It makes more sense for animals to be encountered in the wilderness, but it's never been particularly compelling to me to include a wolf den or an eagle's nest in my sandbox. As a result, animals tend to show up in my games most often as the result of a random encounter check.

I use reaction rolls for every encounter in my games. I modify the reaction roll based on the creature's alignment, so that Lawful and Good creatures are more likely to be friendly or helpful, and Chaotic and Evil creatures are more likely to be unfriendly or hostile. Because animals are typically Neutral or unaligned, their reaction roll is unmodified, and because indifferent is the most common reaction rolled, animals tend to be indifferent towards the player characters. 

This makes sense for animals, but doesn't usually make for engaging gameplay. As a result, animals tend to be little more than wilderness set dressing - the players see a herd of deer and look at them for a while before moving on; they hear wolves howling in the distance and anticipate a fight, but the wolves are simply in the area, doing their own thing - nothing happens.

While unexciting, the even less desirable outcome, for me, is when the animals behave entirely unlike animals - attacking large groups of armed, fire-bearing humans for seemingly no reason and, often, fighting to the death (particularly if the DM isn't using morale rules). I suspect this is more common with inexperienced DMs, who may feel that every encounter needs to be a fight, or who may not know what to do with indifferent creatures.

So, most animals are randomly encountered in the wilderness, rather than in dungeons, and they're either just kind of there, indifferent to the party, or they're bizarro world bloodthirsty killing machines unlike any animals that exist in the real world. But there are things the player characters might do with animals other than observe them or fight them.

Player characters can magically talk to animals, charm them, and bond with them - which are all potentially cool things to do. A random encounter with a frog might be an opportunity for certain player characters to gather information, or, they might want to make the frog their pet (players love pets). But, animals are often also treated as being dumb. It might be fun to talk to a frog, but does it have much to say? The player might delight in having a pet frog, but does it serve any purpose besides being a roleplaying aide?

An encounter with mundane animals might grant other opportunities - they can be killed for food, or for specific resources like fur, blubber, ivory, venom, and the like. I'm not particularly interested in these uses for animals for a number of reasons. 

Food is hardly a concern in my D&D games after 1st-level or so, especially if the party has a druid or ranger among its numbers. It is usually trivial in D&D to forage enough food to feed a party of adventurers or simply carry enough rations to do so. Spells like goodberry and create food and water exist to further trivialize the issue.

I consider this a feature rather than a bug. The exploration "pillar" of the game is about a lot more than whether the characters have enough food and water. I don't want to worry about it past a certain point - if the party has a pack animal, a proficient hunter, or a magical food producer among them, we simply stop keeping track of it. The side effect of this is that there's little reason to take down a randomly encountered deer, which eliminates yet another way of interacting with mundane animals.

I also don't care to establish an economy based on fur, blubber, ivory, or other animal resources. This is probably going on in the background of the setting, but I don't want the players to decide to retire from the adventuring life and pursue a career in ivory poaching instead. That's not the game I'm trying to play - if an animal like a giant spider has a deadly venom the players want to harvest, that's another thing, because the venom has an obvious mechanical benefit. 

One also has to imagine that in a world populated by fantastic mythical monsters, animal materials which are valued in the real world would likely play second fiddle to more fantastic products - a king draped in a lion hide cloak is a cool image, but what self-respecting king in a D&D world wears lion hide when manticores exist?

Which brings me to that other animal-like D&D category of monster, the monstrosity. In 5e, it's a bizarre category for many things, some of which may have animal parts, but are intelligent and can talk (chimeras, sphinxes, the aforementioned manticore, etc.), but also many that are basically the D&D/fantasy equivalent of mundane animals - that is, creatures that are simplistic in their motivations and exist within a larger ecological framework: bulettes, griffons, purple worms, etc. 

This latter group is basically "animals, but a wizard made them." They're a little more interesting than mundane animals - even if they're still used in basically the same boring ways as mundane animals - because they're fantastic. A bulette is a shark that lives underground and can leap 20 feet into the air - that is sufficiently cooler than a real-world shark such that I can use it as is in my games.

So, how does one make animals in D&D interesting? Well, make them fantastic. Humans in the real world didn't always perceive animals through a scientific lens - there were legends and folklore attributed to them. They were viewed as having certain defining traits. 

There is no reason why, in a fantasy setting, owls can't be infinitely wise. A trio of stubborn billy goats might literally guard a bridge that the party needs to cross. A lion might literally be the king of the jungle which the party needs to appease. An elephant might literally never forget.

One tool I like to use in making animals interesting is medieval bestiaries. Specifically, I'm referring to Western Christian bestiaries, because I'm American and my D&D games tend to have that pseudo-European, pseudo-medieval pastiche. 

These bestiaries are a product of the time in which they were written and the people who wrote them. They're written from a Christian perspective, and often have some sort of moral meaning which is tied to God or the devil. Luckily, gods and devils are real, tangible things in most D&D settings, so we can still make use of these bestiaries by loosely interpreting them. 

D&D settings inspired by other cultures should instead use that culture's folklore and mythology for this same purpose. Most animals' Wikipedia entries have a section under "Relationships with humans" which discusses their cultural significance in a variety of regions.

Similarly, a DM can draw on other pop culture references to inform the use of animals in their setting. An entire civilization of human-like apes - akin to that of the Planet of the Apes films - might exist in the setting and be a formidable faction in the world. There may be a Redwall-style civilization of small mammals in the great forests of the world. Domesticated livestock animals across the realm may be embracing Communist ideology, overthrowing their farmer masters and installing porcine party leaders in their stead.

For some reason, animals in D&D are often excluded from the fantasy and magic that pervades the rest of the game. There are flying, talking, spellcasting lizards that can burn entire cities to ash, and chickens that can turn a man to stone with a look, but animals are still used as livestock, pets, mounts, and game. There are hundreds of fantastical, monstrous, and alien humanoid civilizations with their own cultures, languages, politics, and religions, but regular real-world animals still live on the plains and in the forests, hills, mountains, deserts, swamps, and seas, doing exactly what they do in the real world. 

Low fantasy settings do exist, and in those settings it makes plenty of sense for animals to be utterly mundane, but even back in the days when most player characters didn't cast spells or make it beyond 10th-level, D&D was never a low fantasy game, and treating it like one has always been a disservice. There is little reason why every part of the world shouldn't be suffused with the fantastic, and that applies to animals as well. This can all get very silly very fast, but D&D is a silly game, and the silly is often worth embracing.