In reality, when you expand your lungs, you create a low pressure zone in your mouth. This means that you have a pressure in your mouth (and therefore in the straw) lower than atmospheric pressure. At 14.7 pounds per square inch, the atmosphere pushes down on us quite a bit.
Because a straw depends on the surrounding pressure of the atmosphere to push matter into our mouths, it follows that a straw could not work in space. Because empty space is (nearly) a vacuum, there is nothing to force the water into your mouth. However, being that you will probably will never find yourself floating in empty space, a straw would still work on a space shuttle (which you could possibly find yourself in…maybe) because the cabin, like an airplane’s, is pressurized.