In Dragon Age 2, you can order drinks in the Hanged Man. I have ordered a few but didn't notice any difference. Also it doesn't seem to influence any quests or NPCs. Can you get drunk at least or does it just have no effect at all?
If you drink 30 drinks or so and then leave, the next time you enter the Hanged Man, and as far as I know, any time after that, the patrons will all stand, raise their glasses and shout "HAWKE!" I think it's in reference to the sitcom Cheers where they would all shout "Norm!" when he walked in, much like when you have Isabela in your party and pass the Hanged Man, she'll say. "Ah, the Hanged Man, Sometimes you wanna go where everybody knows your name." which is Cheers' theme song. Other then that, there is no debilitating effect. I stood around in one of my playthroughs, where I had massive amounts of coin (400k) and drank somewhere north of 100 drinks, Bartender didn't cut me off, I wasn't drunk, no status changes, no friendship changes, just the patrons bellowing at me whenever I walked in.
I found this forum thread regarding the topic and it seems there really is no effect to the game.
It's simply in there for atmosphere reasons and maybe as a hommage to Bioware's "Mass Effect", because the drinking animation seems to be the same for Shepard and Hawke.