When you have a GridViewDateTimeColumn in the RadGridView and enter in edit mode, you are allowed to clear the current date (set it to null) pressing the Clear button in the popup calendar. However, this functionality is not available in the RadDateTimePicker control.

Workaround:

 public Form1()
 {
     InitializeComponent();
     this.radDateTimePicker1.NullText = "Empty";

     RadDateTimePickerCalendar calendarBehavior = this.radDateTimePicker1.DateTimePickerElement.GetCurrentBehavior() as RadDateTimePickerCalendar;
     calendarBehavior.Calendar.ShowFooter = true;
     calendarBehavior.Calendar.ClearButton.Click += ClearButton_Click;
 }

 private void ClearButton_Click(object sender, EventArgs e)
 {
     this.radDateTimePicker1.DateTimePickerElement.SetToNullValue();
 }