N-layered application structure in ASP.NET MVC 5
It's looking really good.  Some things I might consider that aren't necessary but could help move the code to some better abstractions and hence allow for easier unit testing of features include.


Abstracting your service away from UI related actions by removing the dependency on HttpContextBase.  It looks like all you are using it for is to obtain the IAuthenticationManager so I would pass that into your Login/Logout methods instead.

interface IAccountService
{
    bool Login(IAuthenticationManager authenticationManager, string userName, string password);
    bool Logout(IAuthenticationManager authenticationManager);
}

public bool Login(IAuthenticationManager authenticationManager, string userName, string password)
{
    var user = userManager.Find(userName, password);

    if (user != null) {

        authenticationManager.SignOut(DefaultAuthenticationTypes.ExternalCookie);
        authenticationManager.SignIn(userManager.CreateIdentity(user, DefaultAuthenticationTypes.ApplicationCookie));

        return true;
    }

    return false;
}

public void Logout(IAuthenticationManager authenticationManager)
{
    authenticationManager.SignOut();
    // NOTE:  Now you will have to do the session clear in your controller using this approach
        }

If you were using a DI framework you could consider following the DIP by injecting your service into your controller.  There are many DI frameworks out there (Autofac, Unity, Ninject just to name a few).  This would further abstract your controller away from the service implementation details.

// Account service supplied via Constructor injection
public AccountController(IAccountService accountService)
{
    service = accountService;
}

I noticed you have a base service.  I like this approach but I think I would consider again using Dependency injection (or DI) to provide this to your service so that you can provide another level of abstraction and possibly remove your services need for this.  Hence your base service might turn into something like.

// all services inherit this to expose the DbContext
public abstract class BaseService
{
    protected AppDbContext db { get; private set; }

    protected BaseService(AppDbContext dbContext)
    {
        db = dbContext;
    }
}

public AccountService(AppDbContext dbContext) : base(dbContext)
{
    userManager = new UserManager&lt;IdentityUser&gt;(new UserStore&lt;IdentityUser&gt;(dbContext));

}




  NOTE:  If concerned that using Dependency injection means this
  wouldn't work, don't be.  Constructor injection is a walk in the park
  for these frameworks.



As your base service is likely to never make sense just by itself I would consider making it an abstract class to enforce implementation of the service through child classes.
In the past I have liked to abstract my dbContext away behind an interface to help with further abstracting my services and provide for a final piece of the abstraction puzzle.  So in your case a simple example of this would be:

interface IDbContext
{
   IDbSet&lt;User&gt; Users { get; set; }
}

class AppDbContext : IDbContext
{

}



By doing this you can now inject your context into your services as an interface.  Hurrah!