Oobleck

This one's a classic.  Combine cornstarch and water in approximately equal proportions. And if you want, a little food coloring. When you start playing with it you'll notice that it's a little .... weird. You can actually grab a handful and pick it up - but as soon as you stop applying pressure to it the oobleck starts to drip out of your hand like a liquid. And if you get a speaker, cover it with plastic wrap and pour on some oobleck, interesting things start to happen.

Why does this happen? Well, oobleck is no ordinary liquid. It is a non-Newtonian fluid. This means that applied stress changes the viscosity.

Viscosity is a measure of how much a resistance a substance has to flowing. Water, which flows very easily, has a viscosity of 0.001 Pascal seconds (Pa s). Molasses has a viscosity of 8 Pa s. Viscosity is due to intermolecular attractions (IMF). Strong IMFs mean the molecules can't slide past each other easily. Larger molecules are also more viscous because they can get tangled up. In a normal Newtonian fluid, viscosity is only affected by temperature (the hotter it gets, the easier the liquids can flow).

In a non-Newtonian fluid, applied stress or pressure changes the viscosity. Oobleck is shear thickening (also called dilatant), meaning as stress increases so does the viscosity. One explanation for this is that the water molecules normally allow the cornstarch particles to slip through. But when a sudden force is applied, the water can't get out of the way and the substance behaves like a solid. Another type is shear thinning (also called pseudoplastic), which is when the viscosity decreases as stress increases. 

Non-Newtonian fluids are surprisingly common in everyday life. Some other examples are paint, ketchup, and silly putty!

EDIT: I went to visit MIT and while wandering around, noticed a screen showing a video explaining this! The explanation is very clear and also involves illustrations so check it out.