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Minecraft can be played as an MMO.
You have to find an online server that suits you. They have differing characteristics (Survivor mode, creative mode, PvP, etc.).
Most servers offer various benefits if you pay for them.
In a sense, it's the best sandbox MMO there is. Compared to Minecraft, a lot of 'traditional sandbox MMOs' like EvE and Darkfall seem to play more like simulators.
For example, some servers allow you to protect (and build on) a certain amont of land. (The down-side with this specific arrangement is that over time a lot of magnificent structures fall empty and become permanent.)