Thanks for your answer, but I have an problem with it. You can find it in
the following code (from the Microsoft Help)

In this code I have placed your code in 'DataGridViewComboBoxColumn
CreateComboBoxWithEnums()'

When running this code there is an error that the value of the
DataGridViewComboBoxCell is invalid.

This is because The King is different from The_King. Is there a solution for
this problem?

The code:

using System;
using System.Windows.Forms;

public enum Title
{
   The_King,
   A_Sir
};

public class EnumsAndComboBox : Form
{
   private DataGridView dataGridView1 = new DataGridView();
   private BindingSource bindingSource1 = new BindingSource();

   public EnumsAndComboBox()
   {
       this.Load += new System.EventHandler(EnumsAndComboBox_Load);
   }

   private void EnumsAndComboBox_Load(object sender, System.EventArgs e)
   {
       // Populate the data source.
       bindingSource1.Add(new Knight(Title.The_King, "Uther", true));
       bindingSource1.Add(new Knight(Title.The_King, "Arthur", true));
       bindingSource1.Add(new Knight(Title.A_Sir, "Mordred", false));
       bindingSource1.Add(new Knight(Title.A_Sir, "Gawain", true));
       bindingSource1.Add(new Knight(Title.A_Sir, "Galahad", true));

       // Initialize the DataGridView.
       dataGridView1.AutoGenerateColumns = false;
       dataGridView1.AutoSize = true;
       dataGridView1.DataSource = bindingSource1;

       dataGridView1.Columns.Add(CreateComboBoxWithEnums());

       // Initialize and add a text box column.
       DataGridViewColumn column = new DataGridViewTextBoxColumn();
       column.DataPropertyName = "Name";
       column.Name = "Knight";
       dataGridView1.Columns.Add(column);

       // Initialize and add a check box column.
       column = new DataGridViewCheckBoxColumn();
       column.DataPropertyName = "GoodGuy";
       column.Name = "Good";
       dataGridView1.Columns.Add(column);

       // Initialize the form.
       this.Controls.Add(dataGridView1);
       this.AutoSize = true;
       this.Text = "DataGridView object binding demo";
   }

   DataGridViewComboBoxColumn CreateComboBoxWithEnums()
   {
// Here is your code
// ------------------
       Array a = Enum.GetValues(typeof(Title));
       string[] myValues = new string[a.Length];
       for (int i = 0; i < a.Length; i++)
       {
           myValues[i] = a.GetValue(i).ToString().Replace("_", " ");
       }

       DataGridViewComboBoxColumn combo = new DataGridViewComboBoxColumn();
       //combo.DataSource = Enum.GetValues(typeof(Title));
// And here too...
       combo.DataSource = myValues;
       combo.DataPropertyName = "Title";
       combo.Name = "Title";
       return combo;
   }
   #region "business object"
   private class Knight
   {
       private string hisName;
       private bool good;
       private Title hisTitle;

       public Knight(Title title, string name, bool good)
       {
           hisTitle = title;
           hisName = name;
           this.good = good;
       }

       public Knight()
       {
           hisTitle = Title.A_Sir;
           hisName = "<enter name>";
           good = true;
       }

       public string Name
       {
           get
           {
               return hisName;
           }

           set
           {
               hisName = value;
           }
       }

       public bool GoodGuy
       {
           get
           {
               return good;
           }
           set
           {
               good = value;
           }
       }

       public Title Title
       {
           get
           {
               return hisTitle;
           }
           set
           {
               hisTitle = value;
           }
       }
   }
   #endregion

   [STAThread]
   public static void Main()
   {
       Application.Run(new EnumsAndComboBox());
   }

}