Nice question! Here's my answer!

No, a magnet will not always fall on the same side--it depends on the magnet and on its environment.

For most magnets in most places, the magnet will fall the same way that a non-magnetic object would fall. This is because the falling magnet will only feel a magnetic force if it is inside a magnetic field. These magnetic fields are created by other magnetic objects or by moving electrically-charged objects. When you are farther away from that object, its magnetic field gets weaker. So even if there is a strong industrial magnet in the next room, you probably won't be able to tell by dropping a magnet.

Still, there are other ways to detect weak magnetic fields. A compass works because the magnetic tip of the needle feels a force from the Earth's magnetic field. Since the core of the Earth is so far away, this magnetic field is very weak. But as long as all the other forces on the needle are weaker, the magnetic force from the Earth will move the compass needle until it is aligned with the magnetic field.

Why doesn't the magnet feel a force from its own magnetic field? When an object is aligned with a magnetic field, it will not feel any force (no matter how strong that field is). This is why the magnet doesn't have a force from its own magnetic field--it is already aligned with it. It's also why the needle of a compass stops moving when it is pointing north, because then it is aligned with the Earth's magnetic field. That's why we say the Earth's magnetic field points north.

It's easy to test your question. You can take a refrigerator magnet and try dropping it starting from different angles. You should see that the magnet will fall just like a non-magnetic object, because it is not in a magnetic field (or, technically, the field is too weak to notice).