On the first flight of the day, after every refueling, and if you have flown through precipitation or the plane is left in the rain, you check the fuel for water and to make sure you have the right kind of fuel. Since water is heavier than fuel, if there is just a little bit of water in the fuel it could cause the engine to stop. You can’t pull over to the side of the road like you can in a car, so you need to immediately deal with the problem. The most likely place for this to occur is on takeoff. If you think fast and switch tanks, you might get lucky and only have water in one tank so you can continue your takeoff. If not, you may need to find a place to land.
In 17 years of flying, I have only found water in the fuel once, and it wasn’t even my airplane. But since it was on Catalina Island, a stopped engine would not have been pretty.
The other reason to check the fuel is that airplanes designed for 100LL do not burn Jet Fuel. Jet fuel is denser than 100LL so it will sink to the bottom of the tank. It is straw colored and somewhat greasy, so you can tell if your plane has accidentally been filled with it, but you really have to be paying attention. It would be easy to miss if you just topped off. There have been incidents when twin-engine planes have mistakenly been filled with Jet A and have either crashed or required expensive fuel system cleaning. Mike Busch's article describes his experiences. After the misfueling of a Cessna 421s, someone did a test to see how easy it is to identify a combination of Jet A and Avgas. It’s fairly hard using standard pre-flight practices. That’s why many people recommend watching the fuel truck if you have a twin-engine plane or one that prominently says “Turbo” on the side.
Many aircraft have rubber bladders to hold the fuel. Most older Cessnas have them. Water can get trapped in the folds of the bladder and get into the engine later when the fuel is sloshed around.
Even if the fuel source is free of water, a tank that is not full can have water condense in it.
Most autogas has some ethanol in it. Water will dissolve in a gas-ethanol mixture and so a slug of water won’t get into the engine like it will in an aircraft engine.
Contamination is less of an issue and is one that is really hard for a GA pilot to determine. You really can’t tell if the fuel is contaminated with other petroleum products just by looking at it.