1st Gen You can only obtain Likitung through an In-Game Trade

In the first generation, there's Pokemon you can only get through in game outsider trades. These Pokemon are Mr. Mime, Likitung, Jynx, and Farfetch'd. You also cannot get a Lapras, Eevee, and the Hitmons in the wild. (Besides the starter and fossils, those don't really count in this case.) However, Likitung & Farfetch'd are available in the wild in Pokemon Yellow only. These four trades are also available in FR/LG.

Why do you think this is? I have also always wondered why these four Pokemon specifically aren't available in the wild in R/G/B.

Technically Lickitung could also be found in the wild in the Japanese Blue version. But as for why GF made it hard to get certain Pokemon, that pissed me off too. Why did Jynx and the others have to be restricted to trades when they weren't special or that powerful anyway?

I think Jynx and Mr. Mime are two great examples of Pokémon that don't make sense to find in the wild. That said, they could have been game corner prizes.

As for Lickitung and Farfetch'd, it was probably a random decision. Some Pokémon had to be exclusive to in-game trades in order to promote interaction with the game world and they drew the short straw. Never liked being stuck with the nicknames though...