SteamOS-based Steam Machines hardware. Among the hardware's beta program eligibility forms is an agreement all beta testers must abide by, which states that Valve "has developed and produced prototypes of entertainment system hardware and software, including a set-top box running custom software and a game controller."
Valve's Steam Machines FAQ also addresses the hardware's to-be-revealed controller, noting that the hardware's various forms will be compatible with mouse and keyboard controls, and that the company will "have some more to say very soon on the topic of input."
Now that we know the Steam Machines' controller exists, we can start cooking up predictions on what it will look like. Our guess: It will have three analog joysticks.