Oh man, talk about a tough call, here's my take on it (all with all story DLC's and most with mods):
1. DAO with all DLC and Awakening (by a tiny margin)
2. DAI and BG2. Too tough to pick between those two.
3. ME3 (even with the god child making little sense) the game was powerful and dealt with the end of life as we know it scenario very successfully. I expected Shep to die so no disappointment for me there.
4. ME2
5. NWN (particularly HoU)
6. DA2 (recycled dungeons really knocked this one down)
7. KOTOR1
8. ME1
9. BG1/ToSC - although I adored this game and I may have more playtime on it than any of the others it was a product of its time and simply doesn't have the amount of companion interaction I have come to love from Bioware. The open exploration was awesome though - and the game was really hard (wyverns - need I say more).
10. Jade Empire - game was okay but just didn't speak to me the way other Bioware games have.
If I had to include games by other companies I would probably put NWN2:MOB in my third slot - it was a great game and far exceeded the original NWN2 which would sit at #6 for me. Witcher would sit at #10, Witcher 2 would be #8. I'm not including Bethesda games on the list, because, although I enjoy them they really are too different from Bioware games to really compare. Stories and other characters are so much weaker but the open world/ do your own thing is so much stronger. Depends on whether I want to save the world with a group of complex companions (Bioware) or go on an endless dungeon crawl for cool stuff while creating my own story (Bethesda).
My one observation across the board is that games have become much easier over the years. I remember struggling on normal difficulty in BG1 and BG2 until I figured out the best way to optimize my party and abilities for each enemy type. Even with Bethesda I died a lot more in Morrowind than I ever did in Skyrim. I don't know if the change is meant to appeal to a broader audience but it is interesting. I normally play most games on hard (after a first run on normal to learn the controls). I've never really found a nightmare/insanity difficulty interesting until recently. Maybe I have improved as a gamer, but I suspect it is more that overall difficulty levels are lower.