The Beer Game has been around since the 60's, before the advent of the term Lean, but it contains many Lean aspects, including kanban and reducing inventory. Players manage a supply chain of beer brewery, namely the retailer, wholesaler, distributor and factory. Only the retailer knows the customer demand and this is determined by randomly flipping up cards. The lack of communication through the supply chain and fluctuation in demand creates a bullwhip effect amongst the players, until they figure out how to maintain good inventory levels using some form of kanban.
Because of it's age and popularity there are plenty of free resources available and it has spawned off several software versions that you can download or play online for free at the MIT website.
You can find all kinds of information for running your own game here. As well, there's a good slide presentation you can use here.
All this seems a little overly complicated for what I'm looking for. My preference generally is for simpler games to show lean concepts. The online version might be worth a look, though.