puoi fare

codice:
Private Sub  DropDownList1_SelectedIndexChanged(ByVal sender As System.Object, ByVal e As eventargs)
        Label1.Text = DropDownList1.SelectedValue
        Label1.Visible = True
End Sub
mettendo

AutoPostBack="true"
OnSelectedIndexChanged="DropDownList1_SelectedInde xChanged"

nella DropDownList.
vedi se ti va bene