I used to farm Attumen in Karazhan every week for the Fiery Warhorse mount. I used to farm Anzu in Sethekk Halls every day for the Raven Lord mount. I used to farm the quest in Brunnhildar Village every day for the White Polar Bear mount. I used to farm a lot of things ...
One of my longest-running farming attempts was for the elusive Time-Lost Proto-Drake. I would fly around The Storm Peaks for hours while working on homework, watching shows on Netflix Instant, waiting for random heroic queues, etc. After a few months of diligent hunting, my determination to find, kill, and loot the reins of the Time-Lost Proto-Drake was incited all the more when a friend just happened to fly past the dragon on his way from Ulduar to Dalaran.
At first, I was upset that the mount I sought so dearly had fallen haphazardly into his hands. Soon, though, I realized that if someone could get the mount by sheer dumb luck, it would be much more likely that I find it through persistence. After I spent several more months farming, however, this same friend just happened to see the shadow of the Time-Lost Proto-Drake flash by while he was questing in The Storm Peaks on the new Worgen mage he created when Cataclysm dropped. When I saw him flying around on his second TLPD mount, that was the last straw for me. I gave up the hunt.
What items, mounts or achievements bring out the farmer in you? How long have you been farming for that seemingly unobtainable something?