Why did Sir Arthur Conan Doyle write the book in first person?

Doyle wrote The Hound of the Baskervilles in the first person voice of Dr. Watson in order to highlight Sherlock Holmes's keen intelligence and genius for analysis. Dr. Watson is an everyman who jumps to obvious—and often wrong—conclusions about almost everything and so acts a foil for the highly talented Holmes. Watson is also endlessly impressed with Holmes's powers of observation, and so encourages the reader to be impressed as well. For example, in the opening to this mystery, Holmes is able to figure out what Watson is doing, although facing away from him. This causes Watson to say, in honest admiration:

I believe you have eyes in the back of your head.

Watson continues to be impressed that Sherlock Holmes can derive the meaning from a walking stick left at his home much more thoroughly and accurately than Watson himself can.
Having Watson tell the story also ensures that the mystery is not revealed too soon. Watson is a sincere man who is easily mislead. He can be clueless. This makes Holmes's revelation of the truth all the more stunning to readers when it occurs.