Pokemon X

I usually do when I get enough pokemon to start forming a basic strategy for my party. The only exceptions are Pikachu from Yellow, and whenever I pick the water starter. I usually turn the water starter into a HM slave. They do get to enjoy the sunlight for a little bit since I usually try to evolve most of my pokemon to their final form.
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"Wherever they burn books they will also, in the end, burn human beings." Heinrich Heine
AKA Couchpotatodx

I did with my grass starter in Black 2. I swapped it out for Keldeo when the starters usefulness was outlived. I just now brought it back out, post-E4, to have it evolve to its final form.
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Not changing this until Capcom either gets their act together or the company goes under (Dragon's Dogma was a good start.)

Once, in my current I boxed Serperior. For some reason I expected him to be better this time than the first time I chose him and restarted the game because he was crap.
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"How the Christ do you expect to reverse-Atlantis an entire city? You're just the Dragonborn, not the Daedric Prince of Civil Engineering." - DocWily

I boxed my Pikachu on a playthrough of Yellow once....... yeah.

Thing is, Pikachu was never my headliner in that game. For some reason I'd always catch and train a Pidgey. Pidgeot was my headliner then, way back.
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Official Sabin and Layle of the Dissidia 012: Duodecim Final Fantasy Board.

Until the 5th gen starters I hadn't, but god are they bad. Samurott is ok, but the other 2 are outclassed even early on. Hell Simisage is as good as Serperior, not that grass is all that good anyway.