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I nicknamed when I first started with Red, stopped completely for whatever reason once I got Silver, and then started again with SoulSilver and haven't stopped since. No idea why I stopped, and no idea why I started again.
If I'm just catching it for the Pokedex I won't nickname, but I do nickname everything that actually goes into my party. I'll typically name them after fictional characters from other things that I like.
As has already been said, it makes the Pokemon feel more "mine".
Pic related, VoltWhite and Black nuzlocke.
