in the beginning, Prof. Oak fights/captures a wild Pikachu, and gives it to you.

Gary starts off with an Eevee
 
Team Rocket is in!!! They have Meowth, Ekans, and Koffing (all of which evolve)
 
It's possible to catch wild Charmanders, Squirtles, and Bulbasaurs (like the show)
 
some cheats don't work in this version
 
Pictures of some Pokemon and Gym Leaders have been improved
 
You can print your Pokedex and Pokemon stickers via the GameBoy Printer
 
Pikachu follows you around (you can see him on the screen)
 
Follows the show more closely than Blue/Red
 
Pokemon evolve at different levels in the Yellow version
 
Some TMs won't work on the Pokemon that they used to work on in the Red/Blue version