I have written an article on the core network structures that are used in games today (as far as I know) and which we use in our game Awesomenauts. I figured this might be interesting to people. 
Here's a short summary:
-Client/server: one player decides everything, the other players send him their actions and he updates them on the gamestate. Lots of work to keep controls from getting laggy.
-Dedicated server: same as above, but the server is not a player but a company-owned computer. Benefit is that the server always has good internet and cannot be hacked. Downside is that it is expensive and requires pro server architecture if you are expecting lots of players.
-Peer to peer: each player manages part of the simulation. No input lag if each player manages his own character, but everyone needs to communicate with everyone causing lots of traffic (Awesomenauts uses this).
-Deterministic peer to peer lockstep: each player simulates the game in exactly the same way. Only need to send player actions (extremely small) but controls are laggy. This requires complex coding tricks to keep the simulation exactly the same. RTS games use this since it allows enormous unit counts with hardly any bandwidth usage.
Here's the complete article:
