From the factory, a car's driveline is meant to withstand a certain amount of power. If you upgrade your car's engine to push beyond that limit, things will start breaking. Technology has changed since 1930, when Raymond Mays' Bugatti, shown above, lost its wheel. Today, most cars use constant-velocity joints, which can cause an entire wheel to come off if they fail.
A car's half-shafts connect the differential to the driven wheels. Each shaft is rated to a certain amount of power it can transfer from the transmission (or differential) to the driven hubs. put together an informative video explaining how these shafts work, where the weak points are, and how to make sure you never break one while behind the wheel.
Though adding massive amounts of power to your car is a sure-fire way to rip a stock driveshaft in half, there are some other things, such as adding a race clutch, that could put more driveline shock into the tubes and cause them to break.
Watch for yourself to see how CV joints operate, and what steps you can take to make sure yours don't fail on you.