The "dog" (a Mabari warhound) is a playable character in Dragon Age: Origins. The Warden first meets the dog in the camp at Ostagar, where he is being treated for the Taint. We never learn the dog's original name, but we do know his former master was killed by Darkspawn, and the dog himself is poisoned by the taint. The kennel master asks for calming the dog so that it may be treated - the Warden seems to have a calming effect on the dog. The kennel master also asks the Warden for help in finding some herbs in the Korcari Wilds which will allow the dog to fully recover.
If the Warden saves the dog, and later asks the kennel master about imprinting the dog, the dog will eventually rejoin the Warden after the battle of Ostagar.
Although the dog is not capable of talking, he is highly intelligent and appears to understand human speech, so there is a lot of playful banter between various party members and the dog, the latter whom yelps or whimpers in response to various quips from others.
The dog has a level and abilities just like any other character.
Some of the dog's abilities include a howl that stuns all nearby enemies, a charge that knocks down its target, and a highly effective talent which sees him diving on his target and biting it repetitively -- a damage over time/stun talent.
If you try to start a conversation with the dog you may ask if he has found anything, at which point he may find gifts you can use on other characters.
Clearly a dog cannot carry any swords or weapons, but the Komari Warhounds may be painted with warpaint which add enhancements to their attributes or abilities. They may also wear different collars that confer special powers.
The dog starts off with 100% approval of the Warden. Unlike other party members, his approval does not change from conversations with NPCs (he doesn't judge how you decide to play the Warden). This makes the dog an ideal "filler" character to take along so that you don't have party members of opposing values who will always have opposite reactions to your actions. For instance, when you wish to impress Morrigan and Sten, who value directness and disliked charity, having the dog will allow you to do so without alienating Alistair and/or Leliana, who value compassion and chivalry.