I miss my first ever Dragonite - got LeafGreen in the gap between Diamond and Platinum, transferred it to Diamond and had a lot of fun with it. Rebooted Diamond for a 4-hour round trip car journey to a shopping centre...where Platinum had just come out and my mum was feeling generous. Worst. timing. ever.
I generally find more attachment to weaker Pokémon I persevere with for an entire save - so a Munchlax and Buizel on a previous Platinum save. One of my weakest teams ever actually, but I bred the Munchlax for Curse (named him 'Huell' after the Breaking Bad character) and prevented Buizel from evolving because its cute, partnering it with Rotom using Rain Dance and a Damp Rock. Really high probability of failure but great fun sweeping E4, Barry with them. Likewise Castform (sucky stats but constant weather is fun) and Wynaut in separate Emerald saves, the latter is especially tough to use against the AI pre- physical / special split.
My first ever Feebas came in my last Emerald save a few years back - having owned it since debut - when I painstakingly fished spot by spot, then caught about 50 to get the right nature and some half-decent IVs, then completed the game, waited for Blend Master / Guru / whatever he's called to appear then got its Beauty up, evolved and EV-trained it. It was part of my first ever teams to defeat any battle facilities - Battle Dome in Emerald (my all-time favourite), then Battle Tower in HeartGold, all the way up to Gold Print in the latter, with Milotic repeatedly saving me when my frail sweepers were KO'd with its Toxic stall. Salamence from the same save beat Battle Hall for the first time, although I had to erase its bred Hydro Pump move (one of my first breeds since a PC member stole all my Pokémon back when I only had 1 console) for Fire Blast to get past Shedinja, so also counts among my favourites.
Generally any firsts are favourites - first EV-trained, first egg move bred, first IV-bred, first shiny etc. For my most recent Platinum save I eventually bred 9 Pokémon with 31 IVs in relevant stats, solid overall IVs, egg moves, EV-trained them using the Little Cup method then carried through the save with them. But my favourite is Gallade, enemy of the roaming Pokémon - he's a real quality of life improver!