This is like picking your favourite child.... 
1. KOTOR, because as my first Bioware game, it will always have a special place in my heart. Also I replayed it last year and still totally loved it. (Carth is the best Bioware romance ever...)
2. Mass Effect. For me, the first ME had the best main story arch overall. Also the world building was absolutely brilliant.
3. DAI - loooove the setting. Such a joy to be able to roam about Thedas. When my first Inquisitor started exploring the Hinterland and I realized that Ferelden is no longer brown!!! The Emerald Graves make me want to buy a Villa there...The companion characters, most of the main story, all are very well written. Critique would be the villain is weak and the ending too short.
4. Mass Effect 2 (very close to DAI). Overall story was weak, but again the companions and their stories kept me emotionally involved, And it had the best end mission of all Bioware games.
5. Dragon Age Origin - kill me, but I thought the overall story line - kill the Archdemon - a bit boring. But what really pushed it down the list for me were those endless levels you had to fight through, not just the Deep Roads, but the Mage Tower, the Fade, the Old Ruin in the Forest or the Temple at Haven (yeah, I chuckled, when it exploded in DAI!) Still, the Origin stories, the companions, the tragedy at Ostagar and the Landmeet were absolutely brilliant and Loghain was a very, very good villain.
6. Jade Empire - liked the story and the setting (Asian steam punk? What more could one ask for?)
7. SWTOR - I liked playing some of the class stories as a single player game (Smuggler, Imperial Agent and Inquisitor have good story lines), but I was not too enthralled with the MMO aspects and I kept wishing they had made KOTOR 3....
8. DA2 - The premise was promising, I still admire Bioware's boldness to try something new: no shining hero, everyone is pretty damaged and in the end there is no happy outcome. But the implementation just did not do the theme justice and of course the claustrophobic setting did not help either. The ending also was bodged, but that seems to develop into a Bioware weakness...
9. Mass Effect 3 - Ah, what a wasted opportunity, Tuchanka was one of the best and most satisfying mission I ever played in a Bioware game. Everything came together, all the decision I made in the other two games had an impact and emotionally it was heart wrenching. But it was only one mission and the rest just did not live up to it. And then the ending - even the Extended Cut could not make up for that. Still, even that game I played through twice.