class TaskState
{
   public byte[] readBuffer;
   public List<byte> response;


   public TaskState()
   {
      readBuffer = new byte[4000];
      response = new List<byte>();
   }

}





static void Main( string[] args )
{

   var request = HttpWebRequest.Create("http://ya.ru" );
  
   var stream  = request.GetResponseStream();

   var state = new TaskState();

   var taskRead = Task.TaskFactory.FromAsync<int>( stream.BeginRead, stream.EndRead, state.readBuffer,0, state.readBuffer.Length, state );


   taskRead.ContinueWith( (t)=>
    {
              if ( t.Result > 0 )
              {
                       // Так вот не понятно как повторить вызов taskRead, по идее к текущему Task как-то нужно добавить ContinueWith
              }

    }
  
    ....
}

Streams return zero (0) only at the end of the stream, otherwise, they should block until at least one byte is available.

const int BufSize = 0x10;

static async Task<List<byte>> ReadYaRuAsync(Action<int> onProgress)
{
    var result = new List<byte>();

    var request = (HttpWebRequest)WebRequest.Create("http://ya.ru");
    var responseStream = (await request.GetResponseAsync()).GetResponseStream();

    var buf = new byte[BufSize];
    int bytesRead;

    while ((bytesRead = await responseStream.ReadAsync(buf, 0, BufSize)) > 0)
    {
        result.AddRange(buf.Take(bytesRead));

        onProgress(result.Count);
    }
    return result;
}

static void Main(string[] args)
{
    try
    {
        var response = ReadYaRuAsync(Console.WriteLine).Result;

        Console.WriteLine("{0} total bytes read", response.Count);
    }
    catch (Exception ex)
    {
        Console.WriteLine(ex);
    }
    Console.ReadKey();
}

_>const int BufSize = 0x10;

_>static async Task<List<byte>> ReadYaRuAsync(Action<int> onProgress)
_>{
_>    var result = new List<byte>();

_>    var request = (HttpWebRequest)WebRequest.Create("http://ya.ru");
_>    var responseStream = (await request.GetResponseAsync()).GetResponseStream();

_>    var buf = new byte[BufSize];
_>    int bytesRead;

_>    while ((bytesRead = await responseStream.ReadAsync(buf, 0, BufSize)) > 0)
_>    {
_>        result.AddRange(buf.Take(bytesRead));

_>        onProgress(result.Count);
_>    }
_>    return result;
_>}

_>static void Main(string[] args)
_>{
_>    try
_>    {
_>        var response = ReadYaRuAsync(Console.WriteLine).Result;

_>        Console.WriteLine("{0} total bytes read", response.Count);
_>    }
_>    catch (Exception ex)
_>    {
_>        Console.WriteLine(ex);
_>    }
_>    Console.ReadKey();
_>}
_>

   while ((bytesRead = await responseStream.ReadAsync(buf, 0, BufSize)) > 0)
    {
        result.AddRange(buf.Take(bytesRead));
        onProgress(result.Count);
    }

   int bytesRead = 0;
   while ( bytesRead != 0  )
   {
     task = responseStream.ReadAsync(buf,0,BufSize)

     var bytesRead =  task.ContinueWith( t => 
       {
          result.Add(t.Result)           
         
       });

      task.Wait();
   }