圧縮されたストリームを受け入れるとうまくいきます。
HttpWebRequest req = (HttpWebRequest)HttpWebRequest.Create("http://www.bilyoner.com/iddaa/iddaa-liste");
req.UserAgent = "MOZILLA/5.0 (WINDOWS NT 6.1; WOW64) APPLEWEBKIT/537.1 (KHTML, LIKE GECKO) CHROME/21.0.1180.75 SAFARI/537.1";
req.Accept = "text/html,application/xhtml+xml,application/xml;q=0.9,*/*;q=0.8";
req.Headers.Add("Accept-Encoding", "gzip,deflate");
GZipStream zip = new GZipStream(req.GetResponse().GetResponseStream(),
CompressionMode.Decompress);
var reader = new StreamReader(zip);
var page = reader.ReadToEnd();