While not a full-blown computer, as we'd know them today, a Turing Machine is nevertheless an important part of the history of the field, and its design is still studied and referenced today.
You can build working representations of the idea out of everything from computer parts to LEGO, but what's blowing my mind today is that somebody has managed to simulate a Turing machine's workings with a game of Magic: The Gathering.
The idea of my Magic Turing machine is that the players do nothing at all, except when the game offers them a choice.
Once the in-game "machine" has started, processing continues without requiring any choices from the players, with one category of exceptions: Some of the cards in the machine say "You may [do X]. If you do, [Y happens]." In these cases, the machine arranges that the players will be able to do X, in precisely one way. It just requires the players to always choose to take the game up on any options they're offered.
Amazing. Magic players can see the cards necessary for this here. Everyone else, there's a basic overview of how it all works below.
Magic Turing [Magic Turing Machine v4]