Weezing and fungus guys with Spore like Amoongus, Breloom, and Parasect could probably give you asthma.
Smoke related mons like Torkoal might give you Bronchitis or Emphysema if you hang around them too long.
Repeatedly grooming your Furfrou could give you carpal tunnel (and if you don't keep it very clean and pretty, Furfrou will be sad).
Exploud could give you hearing trouble.
Grimer and Garbodor are probably filled with all sorts of nasty chemicals that could fuck you up if you gave them a hug. Also, they might drip gunk everywhere and you coud slip and fall on it.
Slipping and falling on Tropius' banana peels.
Bird types are known for carrying diseases such as bird flu, so bird types might cause you to get sick.
Bisharp is too pointy to touch without proper protection.
