I've noticed recently that I don't have to forward ports for mmorpg's that I play.
I'm thinking about working on a game that people can play online and had a question.
Why is this the case given its a two way socket connection that is constantly sending data back and forth? Doesn't their server need to get through my firewall in order to connect to me?
You don't need to forward ports to access the web either, despite data coming in as well.
When you make an outgoing TCP connection, your NAT router puts the connection in a table, so that when data comes in, it knows what machine in your LAN to send the packet to.
UPnP allows you to tackle many routers. There's also NAT Punch-Through if you have access to a third party that isn't behind a router.
Either way, port forwarding is only necessary if you wish to act as a server (or the sender in a P2P relationship). A client does not need to forward ports.
TCP crash lesson: TCP is a two-way protocol. The challenge is that at least one host needs to initiate. Since within an MMORPG, your own computer is never acting as a server, nobody has to connect to it. All the information about game state is passed through the company's public facing servers that have public facing IP addresses (and hey, maybe they actually use port forwarding there, just to confuse my explanation... but you never have to see their pretty network internals, proxies, and other wizardry.).
Anyway, when you connect to Stackoverflow, you're making one outbound connection that requests data from the server, and then over that same connection you're receiving it back. Same exact scenario, only with a webserver instead of a game.
Everyone mentions TCP, but NAT works for UDP as well: The first outgoing UDP packet associates that source port with the internal IP address, and your NAT device will forward incoming traffic to that port to the correct host on the internal network.
In other words, if your computer requests the connection (outbound) first, the router opens up the port automatically, on the assumption that you're going to want data back. But if you want remote users to connect to your computer without your computer requesting it, the router would normally drop the packets since it wouldn't know where to send them (they were unsolicited). So instead, you need to tell the router to deliver any unsolicited packets at port N to your computer.
Sorry to add another answer so late, and I know one was already accepted, but I personally found the other answers to be more confusing than this simple explanation.