Find out if the temperature of a magnet affects its ability to attract metal. Place one magnet at the edge of a ruler and see how close a piece of metal has to be for the magnet to attract it. Place the magnet in the freezer for several minutes, take it out, and repeat this process to see if it needs to be closer to the metal to attract it, or whether it can attract it from farther away. You can repeat this experiment with a magnet heated on the stove to determine the impact of high temperature on attraction ability.
Make a simple compass with a magnet, a needle, a small piece of cork and a glass of water. Simple rub the magnet over the needle to magnetize it, stick the needle into the piece of cork so that it comes out the other side (the cork should be in the middle of the needle), and lay the needle in the cup of water so that it it parallel to the water's surface. The needle should turn to point in the north/south direction (the ends should face the magnetic poles of the earth). If you'd like, test it out near a real compass to see how accurate it is.
Electromagnets are magnets created by running electricity around a piece of metal. You can make a simple electromagnet by wrapping a length of insulated copper wire around a large iron nail, stripping the ends and wrapping them around a 9-volt battery. The nail with the coiled wire around it will then become a magnet, and you can use it to pick up iron filings. For a more complicated science project, you can test how the process of creating the electromagnet affects its strength. For example, you can try coiling the wire more times or more tightly around the nail, use a longer wire, or use a smaller nail. You can weigh the iron shavings that the magnets attract to find out which is the strongest.