using System;
using System.IO;
using System.Net;

namespace ConsoleApplication
{
  class Program
  {
    static void Main(string[] args)
    {
      DownloadFile("http://www.ya.ru/logo.gif", "logo2.gif");
    }

    public static void DownloadFile(string url, string fileName)
    {
      byte[] fileBytes = null;
      Uri uri = new Uri(url);
      HttpWebRequest httpWebRequest = (HttpWebRequest)HttpWebRequest.Create(uri);
      HttpWebResponse httpWebResponse = (HttpWebResponse)httpWebRequest.GetResponse();
      using (BinaryReader binaryReader = new BinaryReader(httpWebResponse.GetResponseStream()))
      {
        fileBytes = binaryReader.ReadBytes((int)httpWebResponse.ContentLength);       
      }
      File.WriteAllBytes(fileName, fileBytes);       
    }
  }
}

using (System.Net.WebClient webClient = new System.Net.WebClient())
                webClient.DownloadFile("http://site.com/file.txt", "c:\\file.txt");

foreach (string currentLine in System.IO.File.ReadAllLines("c:\\textFile.txt", System.Text.Encoding.Default))
                listBox1.Items.Add(currentLine);