The player can get up to 129 species total in Yellow without trading. Without evolving any Pokémon, and only collecting evolutionary stages that the player can get in the wild / as a gift or purchase / as an in-game trade, the player can get up to 101 species. The Pokémon unavailable without evolving are as follows:
In Yellow, the player can receive a Machamp via trade; they evolve after being traded to the player. Since the player is not responsible for initiating their evolution, some may choose to consider Machamp "acceptable" in a no-evo run - I would, since my personal philosophy is a little more like "Black/White 2 Habitat List" than strictly "no evolution". If Machamp is counted, the number of species is 102.