I implemented a basic Web Api interface to Umbraco (v7.1.6)

Server code:

public class MemberController : UmbracoApiController
{
   [HttpGet]
   public IEnumerable GetMembers(string countryCode)
   {
        return GSKTools.Server.Handlers.MemberHandler.GetMembers(countryCode);
   }
}

Client code (console application):

using (var client = new HttpClient())
{
    client.BaseAddress = new Uri(serverProperties.BaseAddress);
    client.DefaultRequestHeaders.Accept.Clear();
    client.DefaultRequestHeaders.Accept.Add(new MediaTypeWithQualityHeaderValue("application/json"));
    HttpResponseMessage response = await client.GetAsync("Api/Member/GetMembers?countryCode=FI");
}