What InfoSec regulations should one be aware of when dealing with 'live' cross-border communications, or the offline transport of information?
@nealmcb gave some very good examples.
In general, since your question is quite vague, there are two types of laws that you need to consider when "going international":
As Neal mentioned, each of these laws may apply, depending on country/law:
As mentioned, some of the big ones to know about, besides the non-country regulations such as PCI-DSS and depending on industry, are EU Data Protection, Basel II, and the Chinese Firewall.
If you ask a more targeted question, it may be easier to provide more specific answers.
The world is increasingly interconnected, and it is more and more common that actions by people in one country can affect people in other countries and be regulated by laws there.
Here is a brief sampling of some of the issues to consider.