Pokerus
Pokerus actually is a status ailment that benefits a Pokemon, especially when EV training. But since there is a very low chance of gaining one after a battle, its existence where unknown to much of the Pokemon gaming community.
Arpicorns meanwhile were flavor additions. The concept of roaming Pokemon, weight, the addition of day and time, rods and such screams the needs for "specialized Pokeballs" such that catching the said Pokemons may be easy. Yes, an Ultra Ball has a good chance of capturing Pokemon, but with this balls, I think there is a higher rate of capture.
The two types were a welcome addition to the game, especially Dark Types which finally limited Psychic's power. Back in Gen 1, Psychic types were unmatched seeing as Bug is their only weakness and the only real Bug type attack was Twineedle. Therefore, the addition of Dark types and their attacks in Gen 2 was a real welcome to the community, bringing the status of Psychic down.
Like the apricorns, shiny Pokemon were also flavor additions, meaning they don't affect the game so much. In fact, you could finish the whole game without running into a single Shiny Pokemon, excluding red Gyarados. The stats of a shiny Pokemon were no higher than their normal counterparts. They just look good. And, for bragging rights.
However, breeding is the best addition among all others. You could practically catch a single Pokemon, (and a mate) then breed it. You could mass-produce lots of the said species (excluding unbreedable Pokemon and Legendaries). This is good especially when you are hunting for a certain Pokemon with a certain Personality Value (or nature in later generations). also, you could have an offspring with a desired move it would not normally know.
I therefore conclude that breeding for me is the best addition to generation II.