What animals tail sticks up straight when it runs?

Answer 1

A warthog runs with its tail sticking straight up.

A long tailed animal that may also hold its tail vertically as it runs is the coati. See 10 seconds into the video.

Answer 2

One example of an animal with a tail that sticks up straight when it runs is the cheetah. The cheetah's tail acts as a rudder to help with balance and agility during high-speed pursuits. This characteristic helps distinguish the cheetah's running style from other big cats.