I personally have all the DLC and I'd say if you want the whole story to Dragon Age: Origins, get all of them as they do complete the story.
Warden's Keep will grant players access to Soldier's Peak, two new talents and spells per class from the Power of Blood school, two new achievements, and items. In addition, Warden's Keep will include two new merchants and a Party Storage Chest that allows
the player to store additional inventory.
Playtime added: About 1 to 2 hours.
The Stone Prisoner refers to the titular character of this downloadable content, Shale. In addition, the DLC also grants player access to the village of Honnleath, the abandoned dwarven Cadash Thaig, two new achievements, and crystals which act as armor
and weapons for Shale.
Playtime added: About 2 to 3 hours
Return to Ostagar, this downloadable content features the return of the Warden to Ostagar. There, the Warden will discover King Cailan's armor, Duncan's weapons and the motivation behind Loghain's betrayal. In addition, Return to Ostagar will also grant
the player a second chance at recruiting Dog, and one new achievement.
Playtime added: About 1 to 2 hours.
Feastday Gifts: Ten unique Feastday gifts, one for each companion (only available in Origins).
Feastday Pranks: Ten unique feastday pranks, one for each companion (only available in Origins).
Both the Gifts and Pranks have specific items for each companions, some of which are useful (Sten's Butterfly Sword) while others not so (Zevran's Chastity Belt). Use Morrigan's 'Alistair Doll' with said Grey Warden in your party for some amusing interaction.
There are also items, available at Bodahn's merchant shop at your camp, that will affect your characters feelings towards the Warden. Some increase their feelings of affection by 5-10 points, while other decrease by the same amount.
The Darkspawn Chronicles features a look at an alternate history: what if your character had died in the Joining ceremony, and the Grey Wardens marched under Alistair's command instead? The content is a standalone adventure in which you command genlocks,
hurlocks, shrieks, and even the mighty ogres. Includes a unique reward called Blightblood that transfers into your Awakening and Origins campaigns upon completing the DLC. There are three new achievements.
Playtime added: About 1 to 2 hours.
Leliana's Song: A standalone adventure in which you play as Leliana during the mission—and betrayal—that changed her forever. It is years before the Blight, and Leliana is a young bard whose curiosities run more to passion than to the Chant of Light. Her
mentor, Marjolaine, is determined to inflict the Orlesian game of intrigue on Ferelden, and Leliana is eager to please. It is a time of adventure and excitement. And it cannot last. Includes a unique reward called Battledress of the Provocateur that transfers
into your Awakening and Origins campaigns upon completing the DLC. There are three new achievements.
Playtime added: About 2 to 3 hours.
The Golems of Amgurrak: The Warden has come to Orzammar at the request of Jerrik Dace. Jerrik’s brother, Brogan led an expedition into the Deep Roads to find Amgarrak and the long-lost secrets of golem construction. The rediscovery of such a method would
bring great wealth, power and prestige to House Dace, but the expedition has not returned and is now feared lost. Jerrik, along with his trusty bronto, Snug, will be joining the Warden in the search for his missing brother. Players will find other unexpected
companions as they continue on the journey and will need all the help that they can get. There are three new achievements, which will each unlock a unique reward (a necklace, The High Regard of House Dace, a mace, The Reaper's Cudgel, and a belt, Sash of Forbidden
Secrets) that transfers into your Origins and Awakening campaigns.
Playtime added: About 1 to 2 hours.
Witch Hunt is a downloadable content that explores the whereabouts of Morrigan, the Witch of the Wilds, who aided the Warden during the Blight. It is also the final downloadable content for Dragon Age: Origins. There are four new achievements, which each
unlock a unique reward (a two-handed axe, Dragonbone Cleaver, a longbow, The Sorrows of Arlathan, a mage robe, Vestments of the Seer, and a belt, Cinch of Skillful Maneuvering) that transfers into your Origins and Awakening campaigns.
Playtime added: About 1 to 2.5 hours.
(If your character was romantically involved with Morrigan, this ties up that story arc nicely imo).
There are also three other items you can get for Dragon Age: Origins/Awakening, via playing the Dragon Age Flash game, Dragon Age Journeys.
Embri's Many Pockets is a belt available in this self-titled downloadable content. It is available for free. It can be downloaded in-game by players who have completed Chapter 1 of Dragon Age Journeys.
Stats: +5% fire resistance, +5% cold resistance, +5% electricity resistance, +5% nature resistance, +5% spirit resistance
Amulet of the War Mage is an amulet available in this self-titled downloadable content. It is available for free. It can be downloaded in-game by players who have signed up for an account in Dragon Age Journeys.
Stats: +5% fire damage, +5% cold damage, +5% electricity damage, +5% nature damage, +5% spirit damage
Helm of the Deep is a helm available in this self-titled downloadable content. It is available for free. It can be downloaded in-game by players who completed all five achievements in Dragon Age Journeys.
The achievements are to reach the gates of Orzammar, kill two monsters in a single attack, convince the Bard to join the party, defeat and ogre with all party members at full health and to defeat the hurlock emissary on any difficulty level.
Stats: +2 constitution, +10 mental resistance, +10 physical resistance
There was another, available only if you purchase a Dragon Age T-shirt online:
Mark of Vigilance is an amulet available in this self-titled downloadable content. It is available for free. It can be downloaded in-game by players who purchase a Dragon Age: Origins t-shirt from Hot Topic.
Stats: +6 defense, +2% spell resistance, +5 mental resistance
Also, for a limited time, there was available the Blood Dragon Armor:
The Blood Dragon armor set is available in this eponymous downloadable content. It is available without extra cost to players who purchased a new copy of Dragon Age: Origins. In addition, unlocking the Blood Dragon armor set in Dragon Age: Origins will also
unlock it for use in Mass Effect 2. The code on the card located inside the new copy states that the download will expire April 30, 2010, but it has been used well beyond that date as of April 4, 2011.
The Blood Dragon armor set is a powerful set of silverite massive plate adorned with a crimson dragon across the left shoulder. The armor is available immediately, while the gloves, boots and helm can be purchased cheaply from Bodahn Feddic, a dwarven merchant
in your party camp.
I admit, I'm a completionist of sorts, so I have all the DLC for the Xbox version. There's many more, which unfortunately are only available on the PC version, mainly armor/items/weapons etc. The story based DLC, does add to the overall story and any Dragon
Age fan would get them to learn the whole story of Dragon Age: Origins. Dragon Age Awakening, like
Kimieva said, it is a bridge of sorts between Dragon Age: Origins and Dragon Age II... but also it's kind of like a epilogue to Origins. While the story is less in comparison to Origins, for the final chapter of the game it does work.