After being opened or otherwise made available or worked on of course. I was curious about this since a lot of people bring it up and went about trying to find which bosses took the longest. Not going back to stuff like Ragnaros or Nefarian or anything since raiding only really started to become what it is today in Naxxramas, and C'thun went down in hours after being made possible. Not counting Algalon since you couldn't work on him endlessly.
This is Naxxramas through modern day. I don't attempt to explain why it happened as it happened.
#1 Alone in the Darkness - 70 days from One Light in the Darkness. 7th July 2009
#2 High Astromancer Solarian - 59 days from Magtheridon's death. 24th April 2007
#3 The Four Horsemen - 56 days from Gothik's death to D&T's kill. August 25th 2006
#4 Al'ar <Phoenix God> - 48 days from Magtheridon's death. 13th April 2007
#5 The Lich King (Heroic) - 42 Days from Heroic Putricide's death (first pull). March 26th 2010
#6 Kael'thas Sunstrider <Lord of the Blood Elves> - 31 days from Solarian's death. 25th May 2007
#7 Magtheridon - 29 days from the first 70 raid kills. 24th February 2007
#8 Lady Vashj <Coilfang Matron> - 17 days from being unlocked. 29th March 2007
#9 Leotheras the Blind - 16 days from Hydross' death. 4th March 2007
#10 Loatheb - 14 days from Heigan's death. 17th July 2006
#11 tied Heigan the Unclean - 13 days from Noth the Plaguebringer's death. 3rd July 2006
#11 tied Hydross the Unstable <Duke of Currents> - 13 days from Gruul's death. 16th February 2007
#13 tied Archimonde <The Defiler> - 10 days from Azgalor's death. 9th June 2007
#13 tied Gothik the Harvester - 10 days from Instrucotr Razuvious' death. 30th June 2006
#15 tied Mimiron Firefighter 25 - 8 days from Ensidia's KnockKnockKnock kill to Firefighter kill. May 1st 2009
#15 tied Sapphiron - 8 days from Four Horsemen dying. 2nd September 2006
#15 tied Gruul the Dragonkiller - 8 days from Maulgar's death. 3rd February 2007
#18 Reliquary of Lost Souls - 6 days from Gurtogg's death. 2nd June 2007
#19 tied Kel'Thuzad - 5 days from Sapphiron's death. 7th September 2006
#19 tied Kil'jaeden <The Deceiver> - 5 days from the opening of the third Sunwell gate. 25th May 2008
Runner up - M'uru. 4 days from the opening of the second Sunwell gate. 4th May 2008
Thanks to SK-Gaming's handy list of all time world firsts and wowprogress.com.
Now my question to people reading this is do you remember anything I might have missed? Or are there particularly interesting reasons why some bosses on there didn't die even though they should've?
It's also kind of interesting that the early Burning Crusade period seemed to be when bosses stayed alive the longest in general.