This couple, Joey Wheeler & Mai Valentine, are from Yu-Gi-Oh!  They seem to have a very up and down relationship.  They respond to one another's differences by arguing but when push comes to shove they stick together.

In Yu-Gi-Oh!; the story is that 4000 years ago a deadly game involving monsters was sealed away in Ancient Egypt by a powerful pharaoh, in modern times a teenage boy named Yugi who is that pharaoh's reincarnation released the game.  Now him and his friends have to fight the evils of the game.  Joey is a tough-guy and former gangster that grew up on the streets.  He's persistent and has an attitude, he's a bit slow as far as intelligence goes, but tactically speaking he's a genius.  Mai is prissy, bossy, and arrogant.  She came from a family of wealth, but she went out into the world seeking to cure her loneliness.  As far as intelligence goes she's got that of a high school grad with top honors.

(From Joey after she was sent to the Shadow Realm)

Joey: "I'll get you back Mai!"

~~~

(From Mai after her dual with him during the Doom series)

Mai: "You were my best friend and how did repay you by selling you out to some madman who promised me power."