My friend purchased Red so I went for Blue so we could trade with each other to finish the Pokedex. I can't even begin to fathom how much batteries I wasted back then playing it! I also pride myself in figuring out how to 'see' Mew after spending so much time on it, not catch it or in a battle, but after finishing off the Elite Four I noticed that after encountering missingno your Hall of Fame roster would change to random pokemon, do that enough times and Mew will eventually appear in your Hall of Fame in the PC.
My profile pic should answer who my favorite is. ;)