Can the Bitcoin client be used without any incoming ports being opened? I am running bitcoind on the latest Ubuntu 12.10 Quantal Quetzel on amazon's EC2 network.

The security group I have attached to the box only allows port 22 so I can login via ssh.

How is bitcoind able to operate, then?

I started up bitcoind and it says it has 8 connections and is actively downloading blocks... but how? When port 22 is the only opened port on my box?
-confused
Your firewall allows outgoing connections.  

Bitcoind creates 8 outgoing connections (by default), over port 8333.