There’s no hiding a centaur’s lower half, and that’s exactly what’s excellent about them for world-building. It can be too easy to forget that the nonhumans in the party are just that—nonhuman. But centaurs scream fantasy. They move in the PCs’ world—they might even be PCs—but they are always a bit different, a bit other, a bit more.
Half-elves and centaurs get along well: both are elvish but not truly elven; both love nature but often find themselves living uncomfortably amid humanity; both tend to get by serving in itinerant and mercenary capacities. Maximilian (NG male centaur fighter 4) and Jacquith (CN male half-elf rogue 5) are fast friends in Irriden, walking the cobbles arm in arm and frequenting the taverns with outdoor seating for Maximilian. But Jacquith is beginning to acquire debts and obligations to shadier and shadier folk, and as his situation grows direr, he might drag his centaur friend with him.
Most plains centaurs loathe wildfires. But the spotted Fire Runners actually set small ones so that their young males may race them in coming-of-age ceremonies, and to manage the grasslands so that summer lightning strikes do not turn into wild conflagrations. These traditions are watched over by the tribe’s druids and fire shamans, surprising outsiders who expect the latter to be lunatics.
Centaurs do not take well to space travel; there are few ships that can house them in a way that doesn’t feel like livestock. But they are valued for their size and strength in port. Immaculate, tightly planked boardwalks are a sign of a harbormaster who wants to keep his scimitar- and bolas-wielding centaur watchmen happy.
—Pathfinder Bestiary 42