Games that use Peer-to-peer lobbies instead of dedicated servers, more popular with multiplayer co-op games.

Typically, it can be possible to join another lobby, but impossible to host (insofar as other people can't connect to it)

Lets not forget about consoles too. Xbox Live and PSN complain about obstructive NAT configurations and rely upon uPnP to open ports.

Of course they can be opened manually but that assumes some technical experience, and that the ISP provided hardware gives you access to its configuration.

This is also a problem with games using the client/server model where one of the players is the server.

Ubisoft games come to mind. Without UPnP or specific ports forwarded you’ll have limited NAT support which many games will tell you.