I don't have cultures separated by race that much except some halflings, dwarves and the campaign-specific hailene, but I am a huge fan of riding weird things.
Common mounts in the world include gatornis (think moas), utahraptors (called equiraptors because there's no Utah), and giant spiders.
The spiders have given rise to another mount, the fearbred horse, who are raised under giant spider cages so their entire existence is terror and they break, no longer capable of feeling fear at all.
The bigger folks like ogre, trolls and minotaurs tool around on ceratopsians, ankylosaurs and t-rexes.
In the jungles, giant bats are the choice, and in the cold, huge land seals called couaga are thenew hotness.
Of course this is a world with 1860's level tech, so there are also bikes, velocipedes, autocarriages and limited train service are also on the table.
