All account administrators have access to the send / receive logs for the domains in their account. 

This real time log keeps up to the past 48 hours of message history accessible to assist in troubleshooting or updating filtering rules. End users will not have access to these log files. To access the log files you will need to manage a product and then click the "View Message Log" link on the left hand side. 

Each service has a slightly different set of configuration menu items but they all have access to the message logs.