We recently had a server that was receiving mail correctly, although the emails themselves were then never reaching the internal recipients. Checking over the Event Logs we saw the below error:

Level: Error
Source: MSExchangeTransport
Event ID: 15006


Reading on this further it looks to be due to a feature of the Exchange Transport service that monitors system resources called Back Pressure. We were running a little low on disk space so the easiest fix for us was to move the Queue to a different drive, the below sites explain this in full detail so are worth a read if you experience similar.

Microsoft Technet – Understanding Back Pressure
MSExchange.org – Understanding Back Pressure Feature in Exchange 2007
Petri.co.il – Back Pressure: Moving the queue Database in Exchange 2007