I love all the scarlet monastery stuff, just great storylines for that area. I also really like Durnholde keep in Caverns of Time, cause when you go to old southshore in the instance you see characters younger versions like Kel'thuzad and if you go in the inn you can witness the creation of the Ashbringer.

" The instance where I'm not playing World of Warcraft. "

Molten Core. I know Ragnaros is coming back in the expansion but they should have took the old raid and turned it into a new level 85 5/10/20man instance. 
 
My favourite heroic is probably Halls of Reflection or the instances within The Caverns of Time.

I was recently blown away by that first WotLK instance. It's my first time in this expansion pack, and that first instance was pretty well designed and fun. Can't seem to remember the name of it though. Deadmines is probably my favorite WoW instance ever, and I can't wait for the update it's getting in Cataclysm! :)

Blackrock depths for the length of it. I could seriously just wander around in there for hours at 80.
Stratholm for WC3 nostalgia.
Scholomance just because it was cool. I dig it.
 
As for raids...
 
Karazan. It was my first ever raid. Absolutely adored it.
 
The Eye. My only complaint with this one is that I never got a chance to run it up until it was nerfed right before Wrath came out. Kael Thas is possibly my favorite video game boss of all time. The amount of skill and coordination required to do that fight at that time, was just... ridiculous.  I still remember how vent EXPLODED after my guild killed him. One of my fondest video game memories. :D 
 
SSC. Vashj was just a cool as hell fight that took a lot of communication and coordination to finish. Fun times in here.
 
25 man Obsidian Sanctum. Kind of the same story as the last. My guild had been trying to do it with 3 drakes up for awhile, and when we finally managed to get it down after about 3 weeks of 20-30 wipes every night... just... god. That felt so good. Second horde guild on the server to do it too. Big whoop.
 
25 man Naxxramas. I just enjoyed the stupid little random things that happened in this place when I was running it with my guild. Most of the time a shade or something would just come out of nowhere, one shot a healer, and wipe the raid. We could always just laugh about that and get things going again right away.
 
All of those are my favorite. Not going to pick a specific one just because I have so many memories enjoying each one of them individually.

blackrock spire and blackrock depths

Do raids count? If so then Ulduar is one of the best instances that has ever been put into the game. The siege at the start, then fighting Flame Leviathan, and Yogg, countless times.. Untill they nerfed XT-002 that was a great fight as well. ICC is surpisingly good, based on the failure that was ToC. Naxx was a terrible raid, and Wrath in general fucked raiding up the ass. For 5 man's, the first time in Hellfire Ramparts was pretty cool, although the instance itself is kinda lackluster. Deadmines is great, any of the 5 mans in Terrokar, Uldaman was interesting. Scarlet Monastery was great. And Molten Core of course.

There are a lot of great ones but I think my favourite is Caverns of Time, I loved the way it allowed you to go back and not only explore but have an impact on the history of Warcraft. Also, time dragons!

Ulduar is the best thing to come out of this game for a long time.

Scholomance.  Probably because I ran that place a gazillion times and still never got my damn hat.  That and killing undead is my fave.