Every networked game I've seen uses a reliable transmission layer built on top of UDP. Generally there are packets that work as you describe and are fired out to the server (and/or other players) with 'full' state (typically player position, orientation, speed and maybe a few state bytes... with orientation sent more regularly than position and speed). The remainder of packets are sent reliably.

Each game packet is typically packed (and compressed) with other game packets to maximize bandwidth and acknowledgment data for the reliable packets is also compressed into the data stream. Reliable packets take very little additional bandwidth (assuming your UDP connection is not going to lose many packets in normal use). Players will pull ethernet cables for a second to force packet loss if the unreliable packets give them an advantage (ie to allow them to interpolate through a wall or to not register shot hits).