I am often asked why it is not possible to query the number of received or sent messages, I have even come across a Powershell script that counts the messages in a cumbersome way. But there is an easier way:
Count sent messages on day X:
(Get-MessageTrackingLog -Start „03.10.2012 00:00:00“ -End „03.10.2012 23:59:00“ -EventId SEND).count
Count received messages on day X:
(Get-MessageTrackingLog -Start „03.10.2012 00:00:00“ -End „03.10.2012 23:59:00“ -EventId RECEIVE).count
Always enter the start and end date as MM/DD/YYYY. Simple, isn't it?
PS: You can count pretty much anything this way: (get-mailbox).count for example, shows the number of mailboxes