I want to chime in here: if you don't drink wine, buy a fortified wine for cooking. Vermouth, sherry, port, marsala, etc. These have a longer shelf life than other wines and a dollop will add the rich flavor you're looking for. I actually prefer dry vermouth to regular white wine when it comes to cooking (and yes, I am a wino).
I have to say, though, that I ran out of wine and was going to braise a tough old chuck. Hubby said, "I think there's a bottle of dark beer in the back of the fridge." I braised that animal in that bottle of beer and it was to die for! Yummy!