i think my most memorable experience will be the times where i was playing either pokemon platinum with some friends, or pokemon battle revolution. there isn't a whole lot to say about it but because the three of us rarely really get together, it always stuck out as one of the more memorable experiences for me.
i also remember the very first time i met one of my best friends and it was because i brought the Ruby/Sapphire strategy guide i had with me to school and he was really curious about it. good times.
My Wild Ride of 2016. It's not exactly related to the franchise itself, but it is now permanently associated with Sun & Moon for me and I look back on the experience (mostly) fondly.
Actually, the earliest memory I can recall is getting this bad boy and Pokémon Red for my birthday. Played it right away, chose Charmander without a second thought, and made it to Viridian Forest. Sadly I think it took me a couple tries before figuring out how to save the game.
So, the year is 1999 I think, and little me has somehow managed to catch poison ivy on my, er, masculine feature. To take my mind off it, I would often play Pokémon Yellow. One time during that period, my mom took our family to go see a festival downtown and I had my Game Boy with me with Yellow, in case the itching got bad. We ended up having to leave abruptly because I couldn't handle it though. Which was unfortunate. I know everyone else was interested. But this isn't supposed to sound miserable or anything; I think my parents knew it was a long shot but they'd already bought the tickets before I contracted the ivy, and money for us has never been plentiful. They didn't have anyone they could contact to watch me, so ultimately it was just bad timing, no one's fault. I guess it's odd for me to consider this a "favorite memory" but the way I see it is, Pokémon was there for me during a rough time, and if nothing else, it's at least a distinct scenario that makes my life a little more unique. ¯\_(ツ)_/¯
On a more positive note, I still remember when I was first playing Crystal at the age of 7 or 8 or so, and battling Suicune at the Tin Tower. My leg was trembling with nervousness. I was in the zone hard lol
I fell out of the series shortly before FRLG came out, but got back into it in 2008 I think. I was interested in all the Diamond & Pearl stuff; I would read about the new Pokémon and browse Serebii's DP pages on the library computers after school. But didn't have anything resembling the money for a Nintendo DS. So a cool friend of mine offered to give me their Game Boy Advance, along with a copy of Sapphire. And now that I had things like Internet, I found out about so much stuff I'd missed when first playing Ruby, like the Abandoned Ship and the Regi caves. I even encountered my first non-Gyarados Shiny - a Shuppet on Route 121 - but I was not able to catch it due to a lack of Poké Balls. (But we've come full-circle now - I found a Shiny Shuppet in GO two months ago, so we all good.) After playing through Sapphire I started learning about emulators and such, and went back to play Crystal again, as well as Emerald and FRLG since I missed out on them.
I have frankly too many good memories from the Black & White games, but the ones that probably stick out most are catching my first Shiny (a Sandile - and I still have him!), basically camping out with a friend of mine at the DMV at 1 a.m. so I could take my driver's test in the morning (those lines get absurdly long if you're not super early) and playing Musicals to pass the time, and then more recently, my run of White 2 where I really got into Funfest Missions and completed the White Treehollow challenge, which I've said many times now are probably the most fun I've ever had in a Pokémon game, and I still think that.