Leaving the shrimp tail on or off may be a matter of personal preference, but here are a couple of things to keep in mind.
When you leave the tail on, the shrimp is easier to pick up. When I am serving shrimp as finger food (such as the Coconut Shrimp pictured on the left), I leave the tail on—it's like a built-in handle!
The tail also gives shrimp a pretty and more dramatic look, so if I want to highlight them in the dish, I will leave the tail on. But bear in mind that requires the diner to then cut it off, so if the entire dish is in bite-size pieces (not requiring cutting), I am more likely to remove the tail.