Well just like Dead Space and Mass Effect it seems if you have a save file from Dragon Age: Origins(I assume a beaten one) you will have some different options for Dragon Age 2. Some of the decisions you made in Origins will play a role in Dragon Age 2.
Worry not if you haven’t played number one and intend to start on the second. Senior Producer, Fernando Melo said that sense the game spans over 10 years it won’t have huge detrimental effects on the game if you start fresh. They have 3 premade world states you can use as well(meaning different choices made from the previous game) so even if you didn’t like how your game in Origins ended you can pick a different path.
The DLC on the other hand may have some adverse effects depending on how your last game played out. It may just be subtle at first but could potentially become bigger and bigger as more DLC comes out.
Be sure to keep your save files from Dragon Age 2 as it will most likely come in handy in the future!