The first instance I ever ran was Shadowfang Keep with my brother and his friends. I was led by the nose through it and it's a good thing, because I couldn't fight to save my life -- I just wanted to look at everything! To this day, it remains the benchmark for me by which all other instances are judged. When it received its update in Cata, part of me was really disappointed. I had always looked forward to running it on fresh alts, and I never wanted it to change. For the most part, I'm OK with the changes, and it still remains my favorite instance. And now I don't have to make alts to run it.
So what has been your very favorite instance to run? Not raid, mind you -- that's a whole other Breakfast Topic. Just a regular 5-man instance. Do you prefer the old classics, or has something from Cataclysm stolen your heart? None of the Wrath or Cata instances really did it for me, but I really got a kick out of the Caverns of Time instances from The Burning Crusade.
What grabs you when you get to an instance? Is it the setting? The music? The end of a quest line? Or are you primarily concerned with what kind of loot you're going to get out of the deal?