I expect the following consequences in this game:
+ Connor to be a mage you meet in the game and will have his own quest.
+ Changing dialogue to meet either Grey Warden Alistair or King Alistair.
+ Carver/Bethany will show up as Templars/Circle Mages or Grey Wardens in different parts of the game to back you up.
+ Every previous companion who survives gets their own quest, like in Mass Effect.
+ Leliana will claim the Urn of Sacred Ashes cured her if she died in Origins.
+ Sten will be the Arishok if he recovered his sword. Otherwise, he won't be.
+ Dagda's dialogue will be different if you helped her escape Orzamaar but she got out anyway.
+ The Dream Mage from Dragon Age 2 will be in Tevinter.
+ Zatherien's group will be met in the Dalish camp so we'll get different dialogue depending on who did what in Origins.
+ Merril's camp will be present or not otherwise.