I just created new Web API project (using MVC) in visual studio 2015 and for the testing purpose, I ran that project but ended up below error.
After running the project,
It happens because you have an Authorize attribute on your ValuesController
[Authorize]
public class ValuesController : ApiController
Just remove [Authorize]
and try again
EDIT
According to your edit: You should create a new user and login or use [AllowAnonymous]
as mentioned by @Marcus H. Read more about Identity