Catching up some memories:
I remember seeing a Vaporeon in the wild a couple of weeks ago. It's CP was low and IV as well but seeing one in the wild was awesome.
And I've seen a Gyarados twice in the wild. The first one was during the Water Event I believe so that makes it less rare/special but the other one was before or after the Waterevent. it makes you look twice before you believe it.
And a Blastoise, somewhere in the middle of the night in a spot where I often come so I was thinking that it was because of nighttime but it was pure luck.
My first big fish was a Nidoking, just around the corner.
An Exeggutor just in front of my house. I missed it completely but my son saw it fortunately.
A Lapras during the Waterevent. No Snorlax unfortunaltely.
My first Porygon at a Pokestop.
Or catching a Dragonair.
Wobbuffet was also a nice catch. The first time. Now I have 5 or 6.
All these rares had bad CP/IV but that didn't matter.
It were just special moments you once in a while have.
Most exciting though was caching that little yellow shiny Magikarp.