The rarest Pokémon in the games at the moment would have to be:

Shiny Munchlax in Gen 4. Only available through Honey Trees in the wild, it has a 1% spawn rate at only 4 of them in the whole Sinnoh region. Since Honey Trees only spawn Pokémon every 6 hours. Thanks to HT’s calculations, it has been discovered that if you encounter a Munchlax every time and on your 8192 Munchlax you get a shiny (shiny chances are 1/8192 in Gen 4), 49152 hours would have passed. Even though this isn’t the shiny chance, that is still a very long time to be shiny hunting.

Shiny Feebas in Gen 4. In Gen 3, Feebas was already very hard to catch, but Gen 4 made it harder. Feebas only appears at 1 location in the entire game, Mt. Coronet, on 4 tiles instead of Gen 3’s 6. Also, unlike Gen 3, the tiles change everyday as opposed to manually. Plus, it has only a 1/8192 chance of being shiny, again.

Shiny Female Combee. Combee only has a 12.5% chance to be female, and in Gen 4, it has a shiny chance of 1/8192, and it was available via honey trees only. This means, again, you will have a chance to get a Combee spawn every 6 hours. Luckily though, it has a good chance of spawning at Honey Trees, so it’s easier to find a Combee than a Munchlax, but finding a female shiny is tough.

But, the rarest Pokémon is:

Shiny level 100 Magikarp, Platinum, Resort Area. It has only a 1/10000 chance of showing up, +the 1/8192 chance of it being shiny, meaning that the odds of encountering one is 1/8,192,000 chance. It’s the rarest Pokémon in the games, and then add 6 IVs and it’ll be even more rare.