You could also use Extension methods.  For those not familar with extensions I suggest checking the VB and C# documentation.
VB Extension:
Namespace CustomExtensions
    Public Module ListItemCollectionExtension
        <Runtime.CompilerServices.Extension()> _
        Public Sub AddEnum(Of TEnum As Structure)(items As System.Web.UI.WebControls.ListItemCollection)
            Dim enumerationType As System.Type = GetType(TEnum)
            Dim enumUnderType As System.Type = System.Enum.GetUnderlyingType(enumType)
            If Not enumerationType.IsEnum Then Throw New ArgumentException("Enumeration type is expected.")
            Dim enumTypeNames() As String = System.Enum.GetNames(enumerationType)
            Dim enumTypeValues() As TEnum = System.Enum.GetValues(enumerationType)
            For i = 0 To enumTypeNames.Length - 1
                items.Add(New System.Web.UI.WebControls.ListItem(saveResponseTypeNames(i), TryCast(enumTypeValues(i), System.Enum).ToString("d")))
            Next
        End Sub
    End Module
End Namespace
To use the extension:
Imports <projectName>.CustomExtensions.ListItemCollectionExtension
...
yourDropDownList.Items.AddEnum(Of EnumType)()
C# Extension:
namespace CustomExtensions
{
    public static class ListItemCollectionExtension
    {
        public static void AddEnum<TEnum>(this System.Web.UI.WebControls.ListItemCollection items) where TEnum : struct
        {
            System.Type enumType = typeof(TEnum);
            System.Type enumUnderType = System.Enum.GetUnderlyingType(enumType);
            if (!enumType.IsEnum) throw new Exception("Enumeration type is expected.");
            string[] enumTypeNames = System.Enum.GetNames(enumType);
            TEnum[] enumTypeValues = (TEnum[])System.Enum.GetValues(enumType);
            for (int i = 0; i < enumTypeValues.Length; i++)
            {
                items.add(new System.Web.UI.WebControls.ListItem(enumTypeNames[i], (enumTypeValues[i] as System.Enum).ToString("d")));
            }
        }
    }
}
To use the extension:
using CustomExtensions.ListItemCollectionExtension;
...
yourDropDownList.Items.AddEnum<EnumType>()
If you want to set the selected item at the same time replace
items.Add(New System.Web.UI.WebControls.ListItem(saveResponseTypeNames(i), saveResponseTypeValues(i).ToString("d")))
with
Dim newListItem As System.Web.UI.WebControls.ListItem
newListItem = New System.Web.UI.WebControls.ListItem(enumTypeNames(i), Convert.ChangeType(enumTypeValues(i), enumUnderType).ToString())
newListItem.Selected = If(EqualityComparer(Of TEnum).Default.Equals(selected, saveResponseTypeValues(i)), True, False)
items.Add(newListItem)
By converting to System.Enum rather then int size and output issues are avoided.  For example 0xFFFF0000 would be 4294901760 as an uint but would be -65536 as an int.
TryCast and as System.Enum are slightly faster than Convert.ChangeType(enumTypeValues[i], enumUnderType).ToString() (12:13 in my speed tests).