using System;
using System.Collections.Generic;
using System.IO;
using System.Text;
using System.Threading;
 
namespace WriteFile
{
   class Program
   {
      static void Main(string[] args)
      {
         Thread thread = new Thread(delegate()
         {
            using (FileStream fs = new FileStream("file.txt", 
               FileMode.OpenOrCreate, FileAccess.Write, FileShare.ReadWrite))
            using (StreamWriter sw = new StreamWriter(fs))
            {
               while (true)
               {
                  try
                  {
                     fs.Position = 0;
                     sw.WriteLine(DateTime.Now.ToString());
                     sw.Flush();
 
                  }
                  finally
                  {
                     Thread.Sleep(500);
                  }
               }
            }
         });
         thread.IsBackground = true;
         thread.Start();
 
         Console.WriteLine("Press ENTER to exit");
         Console.ReadLine();
      }
   }
}

ReadFile:

using System;
using System.Collections.Generic;
using System.IO;
using System.Text;
using System.Threading;
 
namespace ReadFile
{
   class Program
   {
      static void Main(string[] args)
      {
         Thread thread = new Thread(delegate()
         {
            using (FileStream fs = new FileStream("file.txt", 
               FileMode.OpenOrCreate, FileAccess.Read, FileShare.ReadWrite))
            using (StreamReader sw = new StreamReader(fs))
            {
               while (true)
               {
                  try
                  {
                     fs.Position = 0;
                     Console.WriteLine(sw.ReadLine());
 
                  }
                  finally
                  {
                     Thread.Sleep(500);
                  }
               }
            }
         });
         thread.IsBackground = true;
         thread.Start();
 
         Console.WriteLine("Press ENTER to exit");
         Console.ReadLine();
      }
   }
}