Script to alert if no email has arrived...

This is a vbscript (save as scriptname.vbs) and can be run as a scheduled job:

Dim myolApp 
Dim myNamespace
Set myolApp = CreateObject("Outlook.Application")
Set myNamespace = myolApp.GetNamespace("MAPI")
Set folder = myNamespace.Pickfolder()
Set folderitems = folder.Items

checkdate  = DateAdd("h", -1, now())

count = 0

for each item in folderitems
	 dateStr = item.SentOn
	 if dateStr >  checkdate then
		count = 1
	 end if
next

if count = 1 then
	'newer found in past hour
else
	'no newer mails found
	SendMail "towho", "email@address.com"
end if

Sub SendMail(TheName, TheAddress) 
Dim objMessage, Rcpt 

Rcpt = Chr(34) & TheName & Chr(34) & "<" & TheAddress & ">" 
Set objMessage = CreateObject("CDO.Message") 
objMessage.Subject = "No new emails in the past hour received" 
objMessage.From = """email alert"" <alert@mail.com>" 
objMessage.To = Rcpt 
objMessage.HTMLBody = "No new emails in the past hour received" 

objMessage.AddAttachment strFilePath

objMessage.Configuration.Fields.Item("http://schemas.microsoft.com/cdo/configuration/sendusing") = 2 

'Name or IP of Remote SMTP Server
objMessage.Configuration.Fields.Item("http://schemas.microsoft.com/cdo/configuration/smtpserver") = "smtp.server.com"

'Server port (typically 25)
objMessage.Configuration.Fields.Item("http://schemas.microsoft.com/cdo/configuration/smtpserverport") = 25 

objMessage.Configuration.Fields.Update

objMessage.Send 

End Sub

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Obviously, some strings need to be changed to fit what you want, email address and smtp server also.
Depends on Outlook being installed, the correct profile loading. Depends also on CDO the be working on the server.
Set folder = myNamespace.Pickfolder() also needs to be fixed to the correct folder in the form of
Set folder = myNamespace.Folders("mailboxname").Folders("inbox")
Works best in Exchange/Outlook environment, but also POP3 if auto retrieve has been set (just don't run the script only once per hour, since it might needs to retrieve messages that are only "seen" during the next run)