Have you ever looked at that little sticker on the windshield and wondered how far you can really push it before you have to pull into a service shop and pay the $40 to change the oil? Of course you have. Well, you should absolutely stop, because you're not only risking the well being of your car, but your own safety as well.
The concept of engine oil is pretty simple. It keeps all of the moving parts lubricated, so none of them are stuck rattling around and bashing into things they shouldn't be. Oil also keeps the engine clean and transfers heat away from engine, keeping the whole setup from melting down.
Now reverse everything in the previous paragraph, and you have a pretty decent understanding for what happen sans oil.