Companions are one of the neatest things about Dragon Age. Not only will they lend you their fighting prowess in battles, but they'll add to the story by piping in now and again during conversations. They'll even give you a bit of advice and most of them have personal quests that you can help them compete. (Not to mention possible romantic opportunities that might arise at camp.)
Here are the possible companions in Dragon Age:
Alistair
Alstair is a sword-and-shield Templar that joins you soon after you reach Ostagar. He's an excellent companion throughout Dragon Age, providing nice tanking abilities while having some offensive prowess. As a Templar, he is especially useful going up against mages as Templar can drain their mana and dispel negative effects.
Gifts: Alistair prefers arcane artifacts and stones.
Personal Quest: Alistair has a sister who you might want to meet.
Dog
Your Mabari war dog will either join you during your initial quest if you are a Human Noble, or just after the battle at Ostagar if you ran the kennel quest. While you may think traveling around with a war dog is a waste of a spot, the dog is actually quite useful. He's a good tank and can train skills like a howl that stuns nearby opponents or the ability to Overrun the opponent, which is a damaging disable.
Gifts: It's a dog. Give him any bones you find.
Personal Quest: None.
Leliana
Leliana is a semi-ditsy bard that will join you in Lothering. Simply enter the tavern and defeat the guards, but be merciful and allow them to live. She starts out trained in the bow, but can easily be cross-trained to duel wield or go another route. She's also pretty handy at picking locks, and this could make her more useful than Zevran.
Gifts: She loves flowers and religious tokens.
Personal Quest: Once she's warmed up to you, ask her how she ended up in Lothering's Chantry, but be prepared to unlock a bit of her darker side.
Morrigan
Morrigan will join your party once the battle of Ostagar is over. She is a handy mage that can buff your weapons with frost and freeze the enemy with Winter's Grasp. She's also a shapeshifter, though shapeshifting might be the least powerful mage specialization considering that you can't cast spells while in an alternate shape. One tip for using Morrigan is to choose heal once she gains a level, which makes her very useful as both a damage dealer and a surrogate healer.
Gifts: She likes old tomes and jewelry.
Personal Quest: After recovering the Balck Grimoire from the Circle Tower, she'll tell you of her findings.
Oghren
Oghren is a beserker warrior who joins you during the Paragon of Her Kind quest just before you enter the Deep Roads. As a beserker, Oghren dishes out a lot of damage and is perhaps a better choice for a DPS tank than Sten, though you can get Sten much earlier.
Gifts: Oghren loves the liquor, so if it is drinkable, give it to him.
Personal Quest: Ask him about a woman named Felsi and then head over to the Lake Calenhad docks.
Shale
Shale is a golem you pick up doing a quest that takes you to Honnleathe. The quest comes with downloadable content that is free for those who purchased the full game. Shale is an excellent tank, able to take a lot of damage and dish out quite a bit of damage in return. This makes his good as the lone tank or in addition to another tank like Alistair.
Gifts: Shale loves remarkable gemstones.
Personal Quest: Shale has some business in the Deep Roads.
Sten
Sten is a two-handed warrior and makes a great starting companion if you are looking for another tank alongside Alistair early in the game. He can be found in a cage in Lothering and freed by speaking to the Mother in the Chantry. Simply bring along Leliana to make sure the Mother trusts you.
Gifts: Sten loves paintings.
Personal Quest: Sten is looking for his sword.
Wynne
Wynne is a spirit healer that can be found on the first floor of the Circle Tower. She's sealed up the rest of the tower with a shield, but will agree to let you pass if you help her rid the Tower of the blood mages and demons. Since she's the best healer in the game, she is extremely handy to have in your party, which makes the Circle Tower quest very attractive once you leave Lothering.
Gifts: Wynne is a scholar and likes items such as the Fancy Scroll and Tattered Notebook.
Personal Quest: Once you are in good with Wynne, her personal quest will start in a random encounter in which she collapses.
Zevran
Zevran is a rogue assassin who is charged with killing you. He's set a fiendishly wicked trap for you, but should you win, you'll have the opportunity to spare his life and invite him to join you. You'll know when he's on your trail by a cutscene showing Loghain hiring him. From that point on, be prepared for a random encounter.
Gifts: Zevran likes gold bars and leather armor.
Personal Quest: None besides romantic escapades.
Loghain
Loghain is a sword-and-shield tank who will join your party should you spare his life and offer him the chance to become a Grey Warden. However, doing so will cause Alistair to leave in disgust.
Gifts: Loghain loves history.
Personal Quest: None.
Dragon Age Companions - Who's best for your party?
For a warrior, you can easily choose to go with either two tanks or two mages. If going with two tanks, Alistair is great if you are going to go with DPS, but if you want to be the main tank, you might find Oghren or Shale more to your liking. Otherwise, you can just load up with Morrigan and Wynne and let them blast your enemy while you bash them upside with your shield.
For a rogue, going with two tanks is best simply to give you plenty of opportunities to do what you do best: backstab. However, if you go Ranger at lvl 7, you can simply summon an extra tank, which works great for bringing along Morrigan and Wynne. You can even think about adding Leliana to the party and letitng her focus on bows and picking locks, which means you don't have to waste abilities to enhance lock picking.
For a mage, you can either go with two tanks and a rogue, which means you'll want to at least get the heal spell to keep people alive, or you can join with Wynne as the healer, which leaves you to dish out the damage. Be aware that Wynne won't like it if she finds out that you are dabling in the blood magic. If going two tanks, Alistair and Shale make great companions. Every mage needs a golem, right?
Dragon Age Information
Dragon Age: How to give a companion a gift
Dragon Age Tips and Strategies
How to Unlock Dragon Age Class Specializations
Companion Gift Guide