These three creatures probably hold the award for strangest retired pets. All three of them are summoned as part of the daily Oracles quest "A Cleansing Song".
The Spirit of Ha-Khalan is a ghostly, partially transparent crocolisk; the Spirit of Atha is a ghostly hydra, and the Spirit of Koosu is a green slime or ooze.
Between Patch 3.0 and Patch 3.0.8, all three of these creatures could be tamed -- because all three of them were labeled as crocolisks! Even now they retain the croclisk family diet, talent tree, and skills.
The Grimtotem Spirit Guide, aka the ghost wolf, is perhaps the most famous retired pet in WoW.
This little wolf was an unlikely hunter pet from the beginning: it is summoned by an NPC and only lives for about 8 seconds before falling over dead. And Tame Beast took 20 seconds to cast ...
But despite this, the ghost wolf could indeed be tamed when it was first introduced in Patch 2.3. Excited hunters spared no expense, buying equipment and recruiting friends to help shorten their cast times so they could complete Tame Beast before the wolf died. And many were successful.
Unfortunately, after several weeks Blizzard decided to correct their mistake, even though they had previously said that they would leave the wolf alone. A hotfix temporarily removed the wild Grimtotem Spirit Guides from the game, although hunters who had already tamed one did not lose their pets.
These wolves reappeared in Patch 2.4 as Grimtotem Spirit Wolves, but they can no longer be tamed.