From what I see (haven't actually tested each one under many different scenarios) this does not really depend on the kind of game. With games with lower numbers of connections, simple blocking socket I/O will suffice. Though if you want a larger number of active connections, you're going to want to use a more efficient management system, such as asynchronous sockets. If using .NET, this is a very easy task. When it comes to MMO-size server, many will strongly suggest looking at IOCP if the backbone server is using Windows and has multiple processors / a processor have multiple cores.

Asynchronous sockets are better than non-blocking performance-wise due to the fact that you do not have to constantly poll them. Instead, you will be "told" when an event happens, and its up to you to decide when to take care of it.

The Forum FAQ talks about this.