At first I thought there is not that many to choose from but after pondering it some more, there really is a lot of couples out there in video gaming. Simple choice for me today though:

Monkey and Trip - Enslaved: Odyssey to the West - Xbox 360, PS3

Although their relationship doesn't get off to a good start (she enslaves him), as the story progresses this changes vastly. The voice acting, dialogue and animation work together seamlessly to bring these characters to life and create a believable relationship which I could get on-board with. Not only that, both characters depend on each other and Trip proves her worth regularly and never becomes annoying. This developers is how you do NPC escort stuff, make me care about the character I'm saving!