Neodymium magnets are really strong. The larger they get, the more careful you need to be to avoid being pinched or struck from the force of their attraction. This video from Magnetic Games cautiously explores what can be done with a large one, including some diamagnetic levitation with a small magnet between two cylinders of bismuth. More from wikipedia:
A neodymium magnet (also known as NdFeB, NIB or Neo magnet), the most widely used type of rare-earth magnet, is a permanent magnet made from an alloy of neodymium, iron and boron to form the Nd2Fe14B tetragonal crystalline structure. Developed in 1982 by General Motors and Sumitomo Special Metals, neodymium magnets are the strongest type of permanent magnet commercially available. They have replaced other types of magnets in the many applications in modern products that require strong permanent magnets, such as motors in cordless tools, hard disk drives and magnetic fasteners.
Even very small neodymium magnets should be handled with care. They aren’t toys, but do make for some great experiments. Next: Dropping a neodymium magnet through a thick copper pipe and how to make simple homopolar motor race cars.