Excel autocomplete/ suggestion list. Not a drop down

That's because that's not how data validation works in excel. You need to use an active X control. Refer to the Contextures data validation page in general and her ComboBox Data Validation and ComboBox Depend examples in particular.

Update

If you do use her examples, replace the TempCombo_KeyDown event handler with TempCombo_KeyUp. At least on my excel (excel 2003 SP2) it crashes.

More gory details about the example I pointed you to:

I'm not sure why changing TempCombo_KeyDown to TempCombo_KeyUp works, but it may be related to KeyCode. MSDN implies that KeyCode is actually a pointer and is for all practical purposes passed by ref, even though the signature says ByVal. The crash always happens on the End Sub line of TempCombo_KeyDown.

This is just guessing on my part, but by processing the KeyDown event, after the new cell is activated, if it has TempCombo, then the object is activated & can process the KeyUp event. If the target cell doesn't activate TempCombo, the KeyUp event has no valid object reference and you get a nasty crash.

As i mentioned in the comments, the only way to do this would be with VBA.

Here is one option. I've added comments throughout the code. This assumes that you are using a named range for the validation list named "List" and that it is on the same sheet as the cells being validated.

Option Explicit

Private Sub Worksheet_Change(ByVal Target As Range)

    Dim cell As Range
    Dim isect As Range
    Dim vOldValue As Variant, vNewValue As Variant


    Set isect = Application.Intersect(Target, ThisWorkbook.Names("List").RefersToRange)
    If Not isect Is Nothing Then
        ' Get previous value of this cell
        Application.EnableEvents = False
        With Target
            vNewValue = .Value
            Application.Undo
            vOldValue = .Value
            .Value = vNewValue
        End With

        ' For every cell with validation
        For Each cell In Me.UsedRange.SpecialCells(xlCellTypeAllValidation)
            With cell
                ' If it has list validation AND the validation formula matches AND the value is the old value
                If .Validation.Type = 3 And .Validation.Formula1 = "=List" And .Value = vOldValue Then
                    ' Change the cell value
                    cell.Value = vNewValue
                End If
            End With
        Next cell
        Application.EnableEvents = True
    End If
End Sub

You can also download the example spreadsheet I put together to test this out. (Contains macros!)