Are there any non-metal objects that are attracted by magnets?
Oxygen, for one. In its gaseous state it moves too fast to be affected, but liquid oxygen can be trapped between the poles of a magnet:
Materials can be broadly classified into three sets:
Diamagnetism: All materials are diamagnetic, but their diamagnetic propoerties are easily masked by paramagnetic/ferromagnetic nature. Diamagnetism is the property of an object to be weakly repelled by all magnetic fields. doesn't matter if its near a north or south pole. It will always be repelled. With stronger magnets, the "weakly" becomes less weak, and we get levitating frogs:
Yup, that's a live frog, but more importantly(except to the frog I guess), he's diamagnetic. And he floats in the magnetic field--poor chap must be confounded.
Paramagnetism This is basically the opposite of diamagnetism. Paramagnetism is the property of a material to be attracted towards a magnetic field--again, it doesn't matter north or south. The strength of the attraction varies widely, but its always greater than the diamagnetic repulsion, and generally much less than ferromagnetic attraction. Paramagnetism is only observed in materials with unpaired electrons. Oxygen is paramagnetic (so is diatomic boron), so its attracted by the magnetic field. Note that not all metals are paramagnetic--in fact many are just plain diamagnetic materials (not sure of this)
Ferromagnetism: This is the property of a material to get permanently magnetised. Only a few elements are ferromagnetic (iron, cobalt,nickel, neodymium, and a few others). These are generally strongly attracted to a magnetic field.
There are many non metals attracted to magnets. Oxygen is an example, which is demonstrated in this youtube video. The property of being attracted to a magnet is called paramagnetism if you'd like to search for more about it.
Sticking to ferromagnetism, http://en.wikipedia.org/wiki/Ferromagnetism#Ferromagnetic_materials has a list of ferromagnetic materials. Several metal oxides are ferromagnetic - I don't know if you'd consider these to be non-metals.
Interestingly, the article claims that a lithium gas can be made ferromagnetic, though this seems a bit esoteric, and I don't know if it would actually be attracted to a magnet.
In the presence of magnetic fields, the non-magnetic material magnetize. There are three types of magnetization: ferromagnetism, paramagnetism and diamagnetism. The most interesting example is ferromagnetism. Non-magnetized iron (latine ferrum) is composed of small domains - domains are little parts of material that act like small magnets, but since domains' magnetic fields are oriented in different directions, net magnetism of non-magnetized iron bar is about zero. In presence of magnetic field, these domains align themselves in the direction of outer magnetic field, therefore, non-magnetized material becomes itself a little magnet. And two magnets attract each other with opposite poles.
Magnetic field is always generated by moving charges. Two primary reasons for magnetic field generation are due to motion of an electron around nucleus and rotation of an electron around it's own axis which is called spin. If we take any atom and place it inside of a magnetic field it will interact with it due magnetic field generated by motion of electrons. The strength and type of interaction depends on the electronic shell structure.