QUOTE(Alanis @ Jul 10 2009, 02:54 PM)

if my customer

send spam through our mailserver

, can I stop it?

Which lays?
Yes. As already noted...
QUOTE(Alanis @ Jul 10 2009, 02:54 PM)

Am I responsible

if he send spam
If you are aware of the problem then, yes, you are responsible. Once you start getting warnings that spam is flowing you should take action.
QUOTE(Alanis @ Jul 10 2009, 02:54 PM)

or download films or games protected by copyright??
I guess that depends on the law in your country. But you won't get listed in a spam BL for this.
Andrew