In our company we have a small business router (Cisco RV082) on which we are using its standard configuration (block all incoming traffic). We also have an SMTP relay configured (using WS2008R2) so that our internal applications can send email through google apps (which requires authentication).
The thing is that the server was being used to send spam. We fixed the problem by only allowing the server to relay email from our internal IP address range (10.0.0.0/16).
My concern is that there was a way by which external IPs connected to the network and that underlying problem has not been fixed, but I cannot imagine how these machines connected.