Unless you count the mazoku attempts to return the world to the Sea of Chaos, no. The dragons don't notice most of the other races, though there have been soem conflicts between types of dragons, and them and the mazoku. Maybe some of them think they are already in charge of us, or could be if they cared to be. [Zelgadis seems to find this more amusing than upsetting]

The humans are scattered into hundreds of kingdoms and republics, so any time a kingdom set out to conquer the world, they'd be more likely to fight other humans than random tribes of orcs. Or if a single kingdom decided they wanted to wipe out trolls or beastmen, their neighbors wouldn't take it as an invitation to do the same. A few would probably oppose them on principle; I could see Saillune doing that.

I have no idea about most of the other races. They either ignore humans, like the elves, or aren't ever in large enough groups to really threaten anything larger than a town.