Falling objects

Why do objects of different masses dropped from the same height always fall at the same velocity, and experience the same acceleration? I have some vauge idea, but I'm not entirely sure.

Larger masses have a greater force on them, so you'd expect them to fall faster.

My physics teacher couldn't really explain this without showing me two formulas, equating them, and then cancelling out the "m"s. I'd rather have an explaination that gives me an understanding of what's going on.

Oh yeah, neglect air resistance.

More mass = more force from the gravitational attraction of the Earth. However, the force is distributed over the mass. Since you have more of both, that evens out, and each bit of mass ends up getting the same acceleration.

As an example, suppose you have two cubes of equal mass, and you let them fall right next to eachother. Obviously, they will land on the ground at the same time. Now, suppose you repeat the experiment, except you glue the cubes together (with glue of negligible weight). The object you drop now has twice the weight of either of the cubes you dropped before, when they weren't attached; Intuitively, however, it will fall just as fast.