you need cookies as its used for form autentication:

> The FormsAuthenticationLoginInfo class is used by the
> ClientContext.FormsAuthenticationLogin method by first calling the
> EnsureLogin method to check for authentication cookies.

more detailed info can be found here: goto Authentication section!

http://www.codeproject.com/Articles/268193/SharePoint-2010-Client-Object-Model-Part-1

taken from link above from fiddler you can see where its setting the cookie authentication in bold

> HTTP/1.1 200 OK
> 
> Cache-Control: private
> 
> Content-Type: application/json
> 
> Server: Microsoft-IIS/7.5
> 
> SPRequestGuid: 22e3f795-a5c9-492d-a551-3e950b8f1c10
> 
> **Set-Cookie: WSS_KeepSessionAuthenticated={4e4cffb3-203e-4857-8f5a-90a4b18789a4};
> path=/**
> 
> X-SharePointHealthScore: 0
> 
> X-Content-Type-Options: nosniff
> 
> X-AspNet-Version: 2.0.50727
> 
> X-Powered-By: ASP.NET
> 
> MicrosoftSharePointTeamServices: 14.0.0.6029
> 
> Content-Length: 460

**EDIT**

Ok so now i know your using windows authentication you need to send the credentails using the following:

    clientContext.AuthenticationMode = ClientAuthenticationMode.FormsAuthentication;

    FormsAuthenticationLoginInfo formsAuthInfo = new FormsAuthenticationLoginInfo("MyUser", "MyPassword");
    
    clientContext.FormsAuthenticationLoginInfo = formsAuthInfo;

in your case:

    using (var context = new ClientContext("http:\\WebApplicationURL"))
    {
        context.AuthenticationMode = ClientAuthenticationMode.FormsAuthentication;
        FormsAuthenticationLoginInfo formsAuthInfo = new FormsAuthenticationLoginInfo("MyUserName", "MyUserPassword");
        context.FormsAuthenticationLoginInfo = formsAuthInfo;
        var site = context.Web;
        context.Load(site, s => s.Title);
        context.ExecuteQuery();
        Console.WriteLine(site.Title);
        Console.ReadLine();
    }

or anonymous user:

    using (var context = new ClientContext("http:\\WebApplicationURL"))
    {
        context.AuthenticationMode = ClientAuthenticationMode.Anonymous;
        var site = context.Web;
        context.Load(site, s => s.Title);
        context.ExecuteQuery();
        Console.WriteLine(site.Title);
        Console.ReadLine();
    }

http://msdn.microsoft.com/en-us/library/office/ee535729(v=office.14).aspx