In the first few games of R/B/Y that I played, I didn't really nickname. As I restarted games again and again, I started nicknaming more often. Let's see now...
Red/Blue/Yellow
Squirtle: Poseidon
Charmander: Helios
Bulbasaur: Gaia
Pikachu: Electros
Nidoran (F): Sirena
Nidoran (M): Lapin (as in lapine, the Latin term for a rabbit. He does look rabbity to me.)
Tentacool: Kraken (all of my Tentacool are named Kraken, although I do have a Tentacruel named Magna.)
Vulpix: Kitsune
Zubat: Sonar
And, utterly in keeping with the mythology theme, I had an Articuno nicknamed Lugia. -sweatdrops- I'm such a fangirl.
Silver
Totodile: Aquarius (my theme for this game was going to be the Zodiac, but that kind of went out the window.)
Hoothoot: Athena
Sentret: Scout (from the Pokedex description)
Bellsprout: Ismenos (I wanted to catch a female Bellsprout and name it Ismene, as in Antigone's sister. Instead, I caught a male Bellsprout.)
Sneasel: Nyuura (Japanese name)
Oddish: Atropos
Oddish: Belladonna (atropos belladonna is the Latin name for deadly nightshade)
Spearow: Aire
Ekans: Kobrani
Zubat: Radar (to differentiate from my Yellow Zubat)
Paras: Tochukasu (the type of mushroom growing on Paras, according to its Pokedex entry)
Jynx: Opera (she looks like she's an opera singer to me. I don't know why.)
Skarmory: Stormwing (which, as I think of it, would have been a much better name for a Zapdos)