+1  A: 

It's not too hard if you make your own computer a firewall, then your app connects to a port on your own computer, and that port is forwarded to both the original destination and logged or forwarded on to your spying computer.

Alternatively you can make your other computer the firwall and have it log/forward the info.

Finally you could use a sniffer.

Bill K
A: 

You could hook into the TCP stack, for example, by using the Windows Filtering Platform or its predecessors, or you could substitute the network libraries/calls of that particular process.

Alexander
A: 

SocksCap will probably do the job (if you're OK with establishing a SOCKS proxy at proxy.foo.com).

wordmonger