Dragons should be ignored for this for now as they're specific and fairly common one in that capacity.

Horses (and other equines) are the assumed default as it's what people are accustomed to. Exotic mounts should not be part of this, for example, elephant riding. Camel, deer, elk, etc. can be considered too little different from horse riding. Birds (ostriches or other large birds) are also ridden in real world though mostly in races, not for their practicality, this makes them exotic mount however.