I can't resist a provocative title. These aren't really "genders", but alternative dimensions upon which a species might be organized biologically, socially, or sexually. Galmoxians courtesy of Semiurge.
1. This species has three genders. Titans serve as their habitats like mobile forests. Foresters care for Titans, relieving them of pests and parasites and cultivating a healthy ecosystem. A healthy Titan releases pheromones that allow Foresters to reproduce parthenogenically. Rakes are physically indistinguishable from Foresters, but are predisposed to hyperactivity, curiosity, individualism, and adventurousness. They traverse Titans to romance fresh Foresters. In a successful courtship, they release a pheromone that temporarily transitions a Forester into a Berserker-state, nearly doubling in size and muscle mass and developing reproductive organs to impregnate the Rake, bringing genetic diversity to the Titan's ecosystem.
2. This species has two genders, one like Hominids, and the other like a variety of Trees. Most relationships are either polyanarchic or serially monogamous, and nearly always full of tenderness. Trees navigate the world through spatial reorientation, where the self is a continual growth process operating at a frequency below the Hominids' temporo-perceptual threshold. Their radical differences in how they perceive and operate in the world, and their limited ability to communicate and understand each other, makes their love both tragic and beautiful. Hominids pollinate the Trees and spread the seeds of their fruit, germinated by the enzymes in their saliva.
3. This species are always hatched in pairs. In nature, parents are only able to provide for one sibling, and so they brutally compete for survival. When one sibling inevitably, through luck or circumstance, outcompetes the other to such an advantage that they gain total dominance, the parents will neglect, disown, or even murder the Forgotten sibling in favor of the Chosen sibling. For much of civilization, this practice has been outlawed or frowned upon, and yet the systemic inequality between Forgotten and Chosen is interwoven through the history and persists into modernity.
4. This species has two genders, Lover and Spirit. While one is alive they are Lover, and in death they become Spirit. The vitality of a Lover provides inspiration for Spirit, imparting a portion of their essence inside the Lover so they may reproduce. The unlifespan of a Spirit may be as much as three times that of a Lover, but after each time they impart their essence they undergo significant aging, and each time more so, and it is rare for Spirits to be capable of reproducing more than three times before expiring.
5. This species has the genders of Chess Pieces. They operate like a hierarchical hivemind. Kings are the mind and soul of the hive, and without a King the hive will flounder for lack of thought or inspiration. They are physically limited and must be protected. Queens are powerful like demigods, and often just as petty and needy and prone to in-fighting. Rooks are workers and artisans, Knights are soldiers and first responders, and Bishops are artists and counsel, and all three are asexual. Pawns are weak yet plentiful, and can develop into the other genders as needed, although most Pawns never make it that far in life, or choose not to develop.
6. Galmoxians - Those sultry seducers of the spaceways - do not technically have genders. Or sex. Like all the unusually-intelligent life on their homeworld, they shape new individuals of their species from the primordial and protean slime which pools in its cracks and crevices, through both physical sculpting and bio-electric-chemical interface facilitated through layers of symbiotic micro-organisms.
However there are somewhat analogous societal roles related to a galmoxian's relationship to this sculpting process. Though by no means universal, the most common are typically translated as "fullshapers", who individually create a new galmoxian through the whole process, "raw-workers" who gather the slime, move it to a work-space, and handle the bulkier details, "detailers" who specialize in shaping certain parts of the galmoxian body, and depending on their skill can garner significant fees for this, "students" who oversee and study the creation process without directly participating, and "wreckers" who harass work-spaces, critiquing the creation process and destroying new galmoxians underway in they can breach the perimeter. Stereotypes, expectations, and so on for each role can differ greatly between cultures and classes within those cultures, even while the roles themselves are fairly