A list of tabletop games in which characters have unusually colored hair.
In Dungeons & Dragons, the moon elves of Faerun commonly have white, silver, or bright blue hair and blue-tinted skin, while the gold elves (also called sun elves) may have metallic golden hair and golden eyes. Plus, the bizarre hair, eye, and skin colors of half-dragons and dragonblooded characters, who are descended from dragons Color-Coded Characters (red, green, blue, black, white), or of various planar nonhuman races like the Genasi, who are the offspring of elementals and humanoids. To be fair, Dungeons & Dragons is a fantasy setting and most of these listed races are just that: different races, i.e not even (entirely) human in the first place. This can be transmitted to their half-human children and persist for generations.
In the GURPSDiscworld scenario "A Little Job For The Patrician", published in Pyramid Magazine, the heavily anime-based villain insists his trolls all grow different coloured moss on their heads, so he can tell them apart, and his Igor has implanted blue hair, just because.
In the heavily anime-influenced RPG Mekton, Mike Pondsmith's infamous Lifepath character generation system includes a table for hair color, which includes both more staid, real-life hair colors as well as anime hair colors such as green, purple, pink and, yes, blue.
This is fairly common in Exalted. People from the West often have blue, green, or purple hair, people in the East have green hair, Southerners have red hair (not red hair as in what our world calls orange hair, RED hair)... and that's not even going into the colors of Half Human Hybrids and people who've been exposed to excessive magic. Wyld mutations can theoretically leave someone with hair any color of the rainbow (or, for that matter, with rainbow hair). Abyssal Exalted are often white haired and pretty... the list goes on.
Gnomes in Pathfinder are close kin to fey and often have brightly-colored hair as a result.
While oddly colored hair isn't uncommon in Shadowrun, it's rarely natural. Victims of SURGE, however, can take oddly colored hair as a negative meta-genetic trait. You can even have hair that changes color to match your mood.
Due to the randomization nature of character generation in Maid RPG, while your characters can have brown, blonde, or black hair, you can also have gold, metallic, rainbow, and transparent hair.
The orks of Warhammer 40K are naturally bald, so they use hair-squig implants (a small voracious creature with a colorful furry rear end that bites onto the scalp). In Dawn of War it's even used as a team color spot.
There's an offhand mention in the Geist The Sin Eaters corebook in the entry for [[Splat The Stricken]] of a girl with Green hair. Justified here because her hair was originally normal, but turned green shortly before she died due to copper poisoning in the water supply. After she came back it stayed on as a mark of her death. Part of the point of the line is that similar things could be the case for other Sin-Eaters, including the main characters.