Program.cs

static void Main(string[] args)
{
    // ログイン（Cookie の取得）
    var session = GetUserSession("メールアドレス", "パスワード");

    // マイページ取得（取得した Cookie を付けてアクセス）
    var url = "http://www.nicovideo.jp/my/top";
    var req = WebRequest.CreateHttp(new Uri(url));
    req.CookieContainer = new CookieContainer();
    req.CookieContainer.Add(session);

    string html = null;
    using (var res = req.GetResponse())
    {
        using (var rs = res.GetResponseStream())
        {
            using (var sr = new StreamReader(rs))
            {
                html = sr.ReadToEnd();
            }
        }
    }
}

private static Cookie GetUserSession(string email, string password)
{
    const string path = "https://secure.nicovideo.jp/secure/login?site=niconico";
    var req = WebRequest.CreateHttp(new Uri(path));
    var param = string.Format("mail={0}&password={1}", Uri.EscapeDataString(email), Uri.EscapeDataString(password));
    var buf = System.Text.Encoding.UTF8.GetBytes(param);

    req.Method = "POST";
    req.ContentType = "application/x-www-form-urlencoded";
    req.ContentLength = buf.Length;
    req.Referer = "https://secure.nicovideo.jp/secure/login_form";
    req.CookieContainer = new CookieContainer();
    using (var rs = req.GetRequestStream())
    {
        rs.Write(buf, 0, buf.Length);
    }

    string html = null;
    using (var res = req.GetResponse())
    {
        using (var rs = res.GetResponseStream())
        {
            using (var sr = new StreamReader(rs))
            {
                html = sr.ReadToEnd();
            }
        }
        var cookies = req.CookieContainer.GetCookies(new Uri(path));
        return cookies["user_session"]; // MEMO: 無い場合は null
    }
}