Amava's had the luxury of being a rich lady. Leveling up largely through the pursuit of flowers and ores, she's always had deep pockets. Any time she's needed something, whether it be a sellable quest item, a piece of gear, enchanting mats, gems, reputation items, you name it, Amava pays cash.
The other day, Amava got a new cloak and wanted to slap an agility enchant on there. Requires Greater Planar Essence, Arcane Dust, and Primal Air.
Checking with her accountant (AH Mule), she's got the GPE and AD on hand, but only has 1 Mote of Air in the bank. Mule trots from the Ironforge Bank to the Ironforge AH, only to discover....the horror....zero Primal Air or Mote of Air available. 3 spam messages over Trade over 7 minutes reveals that there's nobody on willing to sell the mats either.
Time to farm.
Amava flys up to the Elemental Plateau and beats up on some mobs until they cough up 9 more Motes of Air. Ended up with 20 Motes of Fire as well, since the mobs were overlapping their patro areas a little.
And that's when I realized that I've never really done all that much focused farming. Sure, I've done endless gathering along the way. But that's casual, just pick them as you go about your business.
When we first started pestering Attumen and my Engineer got the +28 crit scope recipe, I simultaneously went on a massive ranged weapon upgrade fiesta, going through 3 new ranged weapons in about a week. This had me farming lots of Eternium for the scope, if you can call actually consider it farming, what with Eternium being a random addition to a mineral node anyways.
When I became a Leatherworker, I did 2 days of farming to get past a few slumps in leathers or scales that I didn't gather while leveling Skinning and were also not available via AH.
I've farmed Cobra Scales twice to make leg armors for guildies.
And I think that's it for specific, targeted farming.
I've heard horror stories of farming primals before, but for me, it was 15 minutes and 29 Motes of XYZ later.