One of the first experiments I did at my home lab, and the type I've done most often, is the thermite reaction. This is the exothermic reaction between a powdered metal oxide and a pure metal, most commonly between iron oxide and aluminum. The strength of the reaction can be determined by how far apart the two metals are in the Activity Series. For example, a copper oxide thermite should be more violent than a chromium oxide one since copper is farther from aluminum on the series than chromium (and it is, by a lot). Thermite involves a single-replacement reaction, where the more reactive aluminum replaces the other metal in its oxide, resulting in alumina (aluminum oxide) and the pure metal. The reaction is hot enough to occur in the liquid stage, so the products are generally in one solid lump after cooling. Thermite is used in some welding applications, and was used in special grenades in the military.
The most common formula is a mix of aluminum powder and red iron oxide, or common rust:
2Al + Fe2O3 -> Al2O3 + 2Fe
The reaction, as with all thermites, ends with roughly 98% pure molten metal, mostly caked in or surrounded by alumina. Iron is more dense, and so will tend to sink to the bottom of the mix and clump together, resulting in nice-sized iron pieces.
Thermite mixtures require a very high temperature to ignite, so special methods must be used. There are many ways to do this, and after a lot of trial and error I found a very reliable one that has worked for me every time. Make a small pile of potassium permanganate on top of the thermite, and stick a piece of magnesium ribbon down through the middle of it so it extends down into the thermite as well. Pour a little glycerin on top, and stand back. After about 10-20 seconds, the glycerin reacts with the permanganate to ignite and burn at a very high temperature. This is enough to ignite the magnesium ribbon, which will then burn down into the thermite and finally start the main reaction. Seems complicated, but glycerin + permanganate seems to not be hot enough on its own, and magnesium is notoriously difficult to use - you need a blowtorch to light it and it tends to fragment and burn out before it reaches the actual thermite. My method works every time, and doesn't require you to use any bulky ignition sources - just a small amount of liquid glycerin.