Nexus
Temple of the Jade Dragon has been a favorite for me. Really different when it comes to the artistic design of each boss area.
Old UBRS
I started around Siege of Orgrimmar and enjoyed playing it very much.
Mana Tombs without a doubt :P
Halls of Reflection from the WOTLK! Loved the whole lore and ofc the last "Run for you lives" part where you come up against the man himself (and get saved at the last minute cause you are undergeared and missing another 5 -20 people) :)
It has always been, and will always be, Zul'Gurub. You just gotta love those trolls!
well of eternity
My favorite (and I'll get hate because its not the hard part of wrath) has always been Icecrown Citadel. I love that entire story arc, setting, and art design. Also it was the time when I got to actually devote enough time to be in a hardcore raiding guild, an experience I havent had time to have again since.
Karazhan, all the way.
My favorite instance must be Zul'Gurub. It looks awesome, a large Troll village with temples. It also contains two of the best sounds in WoW, used consecutively, Ding!, and Hey! Grats mon!. I personally use this addon which plays those two sounds when you level up or gain an achievement.
ULDUAR!
karazhan love it
Deadmines <3
Personnaly I like the Shado-Pan Monastery.
My favourite is Karazhan. I really like atmosphere there)
Ulduar, hands down.
My favorite dungeon is BRD - the original undivided in wings, you could run it for hours back in the days.As for the raid - definitely Ulduar. That place is amazing, even though I didn't have a chance to run it when it was current
Icecrown Citadel
My favorite instance is Onyxia's Lair because Onyxia was the first drop mount I ever got (on my 2nd try :D)