[yorwba]

If a cup of water at room temperature were on the surface of the earth and every layer of the earth above it wasn't there to compress it (so no atmospheric pressure) the water would violently boil immediately. If the cup is very tall or you're talking about a cup of very cold ice, the water's own gravitational pressure could keep the bottom stable, but to prevent the top from boiling/sublimating off, you'll need a lid to keep it pressurized.

Moving the experiment to a zero-gravity environment doesn't change the pressure considerations much.