Who rules Ferelden?
This is a complicated one - as described above, it depends a lot on your background, your relationship with Alistair, the amount of support you gained from the nobles, and your willingness to show clemency towards Loghain. Alistair can rule alone or with Anora if you opt for a political alliance; he can also rule alongside the Warden if she's a human noble. Alternatively Anora may rule alone or with a male human noble as consort. If the latter, Alistair will be killed, exiled, or stripped of his claim and returned to the Wardens.
The majority of players will be inclined to put Alistair on the throne, here, as he's a popular party member - but if you're roleplaying a ruthless Warden then kicking him out and marrying Anora yourself is an option. Currying meagre support with the nobles leads, in most cases, to Anora ruling alone.
The Battle of Denerim
Here you determine who landed the killing blow on the Archdemon: you, Alistair, or Loghain. If Morrigan's ritual is completed, this is mostly for determining bragging rights. If not, however, this determines who dies. If your Warden died, this is when they did it. Alternatively, Loghain's redemption can occur in this way or Alistair can sacrifice himself to save his friend (or lover).
Dragon Age: Awakening
The fate of the Architect
The Architect is an intelligent, talking darkspawn encountered in the Awakening expansion (and a major character in the second novel.) After contending with the Warden for some time he reveals a plan to pacify the darkspawn and end future Blights. The Warden can choose to continue doing what they do at this point and kill the Architect, or listen to the plan and agree to spare him - perhaps out of a desire to break the cycle of Blights. This is a tough call - kill him and nothing changes, spare him and risk another Blight beginning sooner rather than later. The latter decision, I think, is most likely to come from Wardens with an open mind, an interest in esoteric magic, or simply a desire to see an end to conflict.
Where did the Wardens defend?
At the end of Awakening you have the option to protect either the Warden stronghold of Vigil's Keep, or the city of Amaranthine, from darkspawn assault - though it is also possible to save both if you've been diligent about clearing sidequests throughout the game. Vigil's Keep is a military asset while Amaranthine is full of innocent people - the Warden's decision will hinge primarily on their compassion relative to their pragmatism.
Oghren is the only Origins companion to return in the expansion, which is why he has a separate entry here. He's a dwarf who likes dwarf things, like drinking and fighting and beards and sex. If you like those things too, you probably recruited him.
Oghren's relationship with Felsi
In Origins, it's possible to reunite Oghren with his estranged partner, Felsi. By the time of Awakening they've had a child and his quests revolve around reuniting them and patching up their relationship. Beacon of understanding? You probably made this work. Don't give a shit aobut the personal lives of your companions? You probably busied yourself stabbing darkspawn instead.
The Power of Blood
At the end of this piece of DLC you're offered a new set of abilities if you quaff a blood magic potion of questionable provenance. Hungry for power? Neck it down. Otherwise, best give it a miss. The golden rule for not turning into a monster in Thedas is 'don't put that in your mouth you moron'.
Fate of Sophia and Avernus
Sophia is a demon-possessed former Warden commander; Avernus is a blood mage used by the Wardens to devise new ways to battle the Blight. In doing so, they roped in human test subjects and everything went to hell. In resolving the quest you can slay Avernus and allow Sophia's demon to go free - the evil option - or take no risks and slay them both. On the other hand, if you spare Avernus you can determine the type of research he continues to do: will you let him do whatever he likes, or hold him to ethical standards? The latter is a nice balance of pragmatism and compassion - normally you have to choose between them.
Shale is a dwarven golem with a mind of her own and a really fun party member to have around. She's recruited as a matter of course in this DLC but she can be killed if the Warden sides with Branka at the end of Paragon of Her Kind.
Matthias and Amalia
The quest to activate Shale involves a possessed cat, a man, and his daughter. The exact outcome depends more on how well you finesse the quest itself than any particular moral choice. Killing Kitty with neither Amalia nor her father being possessed is the best outcome, whereas everything else is a compromise in the demon's favour.
At the end of Witch Hunt, many years after the end of the Blight, the Warden tracks down Morrigan. She's standing in front of a mysterious portal called an Eluvian, an elvish mirror that leads... somewhere (read the fourth book.) If the Warden has a good reason to stay behind - a love interest, perhaps, or a really compelling hobby - then you probably allowed Morrigan to go through without you. If the Warden romanced Morrigan or really wanted to meet their old god demon baby, the Warden has the option to enter the Eluvian as well. If you're still mad at Morrigan for trying to get you to knock her up on the eve of the biggest battle of your life, you can stab her and watch as she stumbles back through the portal. Good job, hero.
Next page: Dragon Age 2, Hawke, Companions