Try this.
Sub X()
Dim objOLApp As Object
Dim objMAPI As Object
Dim objOLFolder As Object
Dim objOLMail As Object
Dim datStart As Date
Dim datEnd As Date
Dim lngCount As Long
Const olFolderInbox = 6
Set objOLApp = GetObject(, "Outlook.Application")
Set objMAPI = objOLApp.GetNamespace("MAPI")
datStart = "1/Nov/2008"
datEnd = "21/Nov/2008"
Set objOLFolder = objMAPI.GetDefaultFolder(olFolderInbox)
For Each objOLMail In objOLFolder.Items
If objOLMail.receivedtime >= datStart And objOLMail.receivedtime <= datEnd Then
Debug.Print objOLMail.receivedtime, objOLMail.Subject
lngCount = lngCount + 1
End If
Next
MsgBox lngCount & " messages between " & datStart & " and " & datEnd
Set objOLFolder = Nothing
Set objMAPI = Nothing
Set objOLApp = Nothing
End Sub