My luck is pretty legendary. Let's see...
I clear Sunwell with the boyfriend (two-manning or three-manning, depending on how you see it - three characters, two mine one his, two people controlling them), and the very first time we ran through we not only got all the tier pieces we both were missing on our mains, but Kil'jaeden actually dropped Thori'dal. o_O
Got the white polar bear back in WotLk, completely randomly - I was just passing by, figured "meh, I'll do the daily, not like I'll get anything" - surprise polar bear.
Got the Eye of Sulfuras to drop for the boyfriend - he'd been soloing MC for a long while without a drop (meanwhile I've had my Sulfuras forever), one reset he didn't feel like going so I told him, you cook dinner, I'll run it for you. It dropped.
Got the Vortex Pinnacle drake out of a random normal mode dungeon finder PuG. Pity it was on my alt priest, not on my main, so I'll still have to grind it for my main but, you know, let's not look the gift horse in the mouth...
Got Aeonaxx on the first day of seriously camping him - after getting both TLPD and Aonaxx for the boyfriend, with minimal camping involved. Still haven't seen TLPD for my main, but again, gift horses...
Took me ages to get a Green Proto-Drake out of the stupid Oracle egg... then a few weeks after I got mine, patch 4.1 landed and with it the CTA satchels. And in the process of running my weekly heroics on my main (a tank), I got a satchel to drop me a second Green Proto-Drake. Made for a very happy alt who'd been up until then riding a sparklepony.
Headless Horseman's mount took me a long, long farm the first year of the event, back when it still dropped from the boss. (I and the boyfriend could easily two-man him by ourselves, since we outgeared the encounter massively, so we started paying people for their summons - here, have a picture:
That's about half of that day's corpses, they despawn somewhat fast.) Then a year later, I was running it on my alt and it dropped on the first day and I won the roll.
Similarly, spent ages grinding the Searing Scorchling for the boyfriend, back when it still dropped from Ahune on the first year of the event. Got it for him the last day. Never got mine. Went back a year later, got it first kill.
I've also gotten Anzu to drop (back when it was a druid-only thing) for like... 5-6 people? Not all in a row, but relatively fast (within a month or two of very casual farming, not going every day.) First myself, then the boyfriend, then an alt of mine because I felt like it, and then I started taking friends through for a lark to see if it dropped, and sure enough...
One of my alts, first random heroic ever back at 80, gets Oculus, gets the blue drake out of the bag. (Then a second on her second Oculus, and then a third on her third Oculus, and the spares are still in her bank because I haven't the heart to delete them, and meanwhile my main still doesn't have hers, but hey...)
Boyfriend's trying to gather enough vanity pets to get the Celestial Dragon (150 pets). So off I go farming mobs on an alt that I know hasn't done the
Mechanical Chicken quest, so I can then give it to him. I go to Feralas first, and it occurs to me that I might as well go kill the mobs that drop the
Tiny Emerald Whelpling, you know, just in case, since the boyfriend's still missing that, too. Sure enough, two loops and a half of the lake later, I loot a whelpling. Still no OOX quest starter but hey...
On the opposite end: still don't have the damn turtle mount from fishing. (Meanwhile boyfriend fished like two pools for a lark and got his, grrr.) Still haven't got Illidan to cough up the damn
blindfold. Still no luck winning the roll on the new Amani bear on my main, despite successfully completing the run in dungeon finder PuGs several times. (Meanwhile, one of my alts has it. Figures.) Still haven't seen either of the dungeon dragons drop.
But all in all I can't complain...