>>12700824-Fairy/Grass: These are considered taboo to mate with in most cultures, as they are too bestial, or too much emphasis is placed on their significance to natural traditions or customs. Blissey has gained an interesting sexual culture in urban centers, but outside of them, sexual relations are banned by law or custom.
-Human-Like: The third-most accepted behind Ditto and Undiscovered. Most Human-Like carry out roles in human society, and most, contrary to popular belief, can easily speak human languages. Some such as Throh and Sawk even have campaigned for citizenship, and anti-catching practices. Of course, for every Hitmonlee campaigning, there's a dozens Lucarios as the willing family pet, so the movement is unlikely to gain much universal traction outside of individual cases.
-Mineral/Amorphous: These are more case by case. Mineral species are never bred with, but Amorphous have a few Humanoid Pokemon that are intelligent enough for intimacy. Ghost Pokemon have been among the first in legend to play with human sexuality, first as tricks and then as intimate others.
-Water 2: Banned in most countries, and impossible in many circumstances. Octillery have been known to get frisky with many a Swimmer, but otherwise there are no major sexual encounters.
-Undiscovered: This is where things go case-by-case. Obviously, the baby Pokemon in this grouping are never bred with (legally). As for the mythic Pokemon, there are no laws against having sex with them, but most of the community denies their existence as well, so recorded events of mating are made of legends such as Articuno's Boudoir, or the Lugia Royal Nest. Many a boy and girl adventurer want to become Pokemon masters out of such legends.
tl;dr You can't fuck Pikachu, but you CAN fuck Lucario. The furries can rejoice.