The Tower of the Archmage is hosting this month's RPG Blog Carnival which poses the question "What roles have animals played in your games?". Here are some of the ways I've used animals over the years.
Familiar - One of the things most Sorceror's do fairly early on in their career is to augment their character with a familiar. As well as providing important skill boosts for the traditionally weak low level sorceror, they can be quite useful plot devices for DMs as well. In my last campaign one of the PCs had a cat which had an annoying habit of wandering off and discovering things I wanted the PCs to uncover. Non-magical classes can get into on the action
Animal Companion NPC - Non-magical characters can get in on the supplemental skill action with an animal NPC. Barbarians with tame bears and wolves are not unheard of, Rangers with birds of prey, Elves with dragons etc. They are a common feature in literature, from Samwise Gamgee and his pony "Bill" in The Lord of The Rings to Fitz's bonded wolf "Nighteyes" in Robin Hobb's Farseer Trilogy.
Pets - These animals tend to be more of a quirk than anything truly useful, but can be good plot devices for DM's. One of my current campaign PCs rescued a terrapin from the a streetvendor who was barbecueing them as tasty treats. All credit to him as a player he had us in stitches when in the middle of a rather intense discussion over a round of drinks in a tavern, he reached across the game table to retrieve his imaginary terrapin as it tried to escape.
Producers - All animal companions have the potential for use as a melee weapon, but there are some animals which can have uses beyond the mundane biting and clawing aspects of combat. How about animals such as the humble goose whose feathers make quills or arrow fletchings, the bear that you must kill in the Northern Wastes in order to make a coat to survive a snow storm. In my current campaign there's an Assassin who keeps a tree frog which produces the poison he dips his darts in.
Transport - If you've not run a game where your PCs have bought a lame, stubborn or unrideable horse, or in my case a psychotic spitting camel, then you should even if just for comedic value. Retrieving a loose horse or fending off a bunch of rustlers are also fun sidetreks to relieve the boredom on a journey. I've even created my own Animal Item Cards and Paper Minis to help my players to visualise and manage them.
Animal Hybrid PCs - One of my favourite RPGs is Justifiers which has the "Beta-Humanoid" animal hybrid concept at it's heart. These corporate owned constructs are bred for their congenital abilities which make them extremely useful for exploring new planets for natural resources which their corporate masters hope to exploit. I also used the animal hybrid as a concept for Lizardmen in my campaign, complete with a racial schism which over the centuries as meant that a common ancestor evolved into two distinct species Red Salamankari and Green Salamankari but who share many physical and social similarities including a bloodthirsty animosity towards each other.