Is it worth completing Dragon Age Origins before playing Dragon Age 2?
Solution 1:
From what I've heard, there isn't much impact on Dragon Age 2 from DAO. The story takes place in a different part of the world, and there are only a few side characters that carry over at all, none of which are in your party. So from just the standpoint of enjoying DA2, I'd say no.
On the other hand, DAO is a great game, and DA2 has been getting pretty mediocre reviews, so one could make the argument that you should play DAO first just because it is a better game for less money. =)
Solution 2:
While it's true much of what you do in Dragon Age II isn't directly connected to the plot of Dragon Age: Origins, the game assumes you are familiar with the setting established in Dragon Age: Origins so much so that it completely glosses over a ton of exposition which serves to give meaning to the motivations of the main character and the overall story.
That is, if you don't play Dragon Age: Origins, you're going to find yourself asking "Who cares?" more often than not while the plot unfolds. Dragon Age II will give you the CliffsNotes version of a plot element, but the background behind that plot element is fully explored in Dragon Age: Origins.
Additionally, there's a ton of dialogue points in sidequests and with companions which make reference to the events of Dragon Age: Origins that'll be lost on the person who doesn't play it.
But perhaps the most important reason to play Dragon Age: Origins before Dragon Age II is that it's the better game. Dragon Age II has better gameplay and a much improved user interface, but it's not the Godfather II of the series. You'd be doing yourself a disservice by not playing Dragon Age: Origins in order to play Dragon Age II exclusively.