Pokémon you keep noncompetitively

[The_Emperor]

I usually have a team of pokemon that get first ingame. I only allow myself to have 6 main pokemon (the ones in my team) and I promise myself to keep me until I beat the elite four. That way, it is as if I have bonded with them, making the ending better because it was with those same pokemon. On my pokemon Diamond I have a whole box full of level 100 Arceuses which I use to show off and sometimes trade people who haven't done the event. (I used an action replay when I was younger). I do not believe in something called 'pokemon cruelty' meaning I don't like HM slaves so I never catch a pokemon specifically for teaching HMs (normally. Sometimes I catch a few because the rest of my party can't learn the move)

 

[Lady Vader]

Since 4th gen I always keep around a Tropius/Bibarel pair. Together they can learn all of the HM moves that have ever existed, and if a generation has less than 8 HM moves needed You can give them stuff like Sweet Scent and Dig respectively.

Tropius:
-Cut
-Defog
-Flash
-Fly
-Headbutt
-Rock Smash
-Secret Power
-Strength
-Sweet Scent

Bibarel:
-Cut
-Dig
-Dive
-Headbutt
-Rock Climb
-Rock Smash
-Secret Power
-Strength
-Surf
-Waterfall
-Whirlpool

They're the Dynamic Field Move Duo, only missing minor stuff that doesn't matter at all(Teleport, Soft-Boiled, Milk Drink, and Chatter)

I did the same thing in Generation IV, but it was Charizard and Golduck.

 

[Voltage]

I usually send my in game team to the fancy "Hall Of Fame" box on my X that I never touch, other than to admire them. It's a cool thing to look back on all those boxes with Pokemon from 2004 still existing today in my modern game.

 

[thdhted]

I'm a fastidious Event collector, and have a good majority of the ones after 2009, even if they're noncompetetive. I keep them mostly because they're actually pretty valuable if they're an event from awhile ago, and because of nostalgia reasons. I was really upset when I found out that Pikachu can't keep Surf when transfering it(though I still have one with Fly), but I've still got some of the harder to find ones(legit Mew, Shiny event Hydregion, all three Shiny Dogs, several Japan exclusive ones, ect).

Of course, I also have an (unorganized) collection of shinies, including a Brave, 3 IV Mewtwo(HP/Atk/Def), that I got for giving up an event Deoxys. I actually have a competitive Shiny Terrakion that took me almost a month of RNG'ing to get, alongside a few other shinies (the first ever shiny I bred myself, my first encountered Shiny, ect.)

 

[meowmachine]

I keep most of my non-genned shinies, a few utility mon (Teddiursa with sweet scent, Breloom with spore and false swipe), and pretty much every major starter I've used, and all my Nuzlocke hall of famers (12 at the moment). I also have a full box of level 1 starters for collection purposes. And I have 2 boxes full of Spinda.

 

[Fluke]

I keep my in-game teams and randomly encountered shiny Pokemon.

 

[mertyville]

centain shinies, a flamebody user and HM slaves...everything else will be released after the main story is done.

 

[PsychicAcademic]

Except for too many Eivui when I barely have space in my PC, I don't have the heart to release any Pokemon. I remember my X still has the original team I first had there, including a female Showers I always thought to be mother of my other bred Eivui sisters. I call her Mother Vaporeon.
I even kept my Raichu there, even though when I was playing there she could barely keep up. She is still part of the team.
I respect the storyline team as the seniors and teachers to my custom bred teams.