C#

void UpdateAndRestart()
{
    //Assumes you have already downloaded new exe to myNewExeLoc
    string myNewExeLoc = @"C:\My Folder\myNewExe.new";
    string myCurrentExe = System.Reflection.Assembly.GetExecutingAssembly().Location;
    string myBakExe = myCurrentExe + ".bak";

    if (System.IO.File.Exists(myBakExe))
        System.IO.File.Delete(myBakExe);

    System.IO.File.Move(myCurrentExe, myBakExe);
    System.IO.File.Move(myNewExeLoc, myCurrentExe);

    System.Diagnostics.Process newP = new System.Diagnostics.Process();
    newP.StartInfo.FileName = myCurrentExe;
    newP.StartInfo.Arguments = "/updated" //or whatever arguments you want to pass (not required)
    newP.Start();

    System.Environment.Exit(0);
}

compute "old" name (foo_old.exe?)
delete old named file
rename current file to old named file
rename new file to current file name
run current file
exit "this" image (now the old named file)

void UpdateAndRestart()
 {
     //Assumes you have already downloaded new exe to myNewExeLoc
     string myNewExeLoc = @"C:\My Folder\myNewExe.new";
     string myCurrentExe = System.Reflection.Assembly.GetExecutingAssembly().Location;
     string myBakExe = myCurrentExe + ".bak";
     if (System.IO.File.Exists(myBakExe))
         System.IO.File.Delete(myBakExe);
     System.IO.File.Move(myCurrentExe, myBakExe);
     System.IO.File.Move(myNewExeLoc, myCurrentExe);
     System.Diagnostics.Process p = System.Diagnostics.Process.GetCurrentProcess(); //Change #1
     System.Diagnostics.Process newP = new System.Diagnostics.Process();
     newP.StartInfo.FileName = myCurrentExe;
     newP.StartInfo.Arguments = string.Format("/restart {0}", p.Id); //Change #2
     newP.Start(); //Make sure this is the second to last thing you do
     System.Environment.Exit(0); //Make sure this is the last thing you do
 }
 //Then do this in your Main (or Splash) but do it before you need to muck with the new/old exe thing
 void Main(string[] args)
 {
     if (args.Length > 0)
     {
         switch (args[0].ToLower())
         {
             case "/restart":
                 int oldPid;

                 if (args.GetUpperBound(0) < 1 || !int.TryParse(args[1], out oldPid))
                     break;

                 Process p = System.Diagnostics.Process.GetProcessById(oldPid);
                 if (p != null)
                     p.Kill();   //since you already did all your shutdown stuff before you called this
                                 //it should be safe to just kill the process if its hanging
                 break;
         }
     }
 }