I think of these two as my best pulls ever. Each has a story attached:
For the Honus, I had been bugging my LCS for months about when it was coming in. When it finally did, they gave me first crack at it. First pack...HONUS!
For the Lebron, my GF and I had just come back from the casino where she had won quite a bit. Since I was nice enough to drive her the 3 hours roundtrip, she gave me some money to go buy any box of cards I wanted. It was just about enough to buy 2003-04 Exquisite, so that is what I did.
More recently, until last year I have never, ever pulled a Griffey rookie out of anything. Even when we were playing pack wars with 1989 Donruss early last year I would never get the Griffey. Got a lot grief over this. When 2014 Donruss came out, I bought a box and started cracking it in the shop. As I'm opening packs, I notice, hey there is a buyback auto in here. Looked at the name on the card and told the owner, "Give me a 35pt one touch. I'm not even touching this card". The buyback auto was 1989 Donruss #33 Griffey, auto #9/9.
All of these are in my PC and aren't going anywhere because of the story attached to each.
Bonus best pull I never got story: Back in 2001, I got a redemption for a Rookie Relic TRR-PF Pedro Feliz. Back then, you had to mail them in, so I did that within a month or two of the product being released. Got back a letter from Topps something like: We're sorry, but the card you wanted is out of stock. Please accept this replacement instead. What was it? Rookie Relic TRR-AP Albert Pujols. I'll tell you, 14 years later, I'm STILL looking for that Feliz relic (and the Ed Rogers one). I think I've seen two Rogers on Ebay in that time. Never seen the Feliz one. Still, having the Pujols relic caused me to buy the relic set. I also went on to build the retrofractor set. Took years, but it was fun to do.