Can I use motor oil in a aircraft piston engine?
By motor oil, I assume that you mean automotive motor oil. In that case, it's a bad idea for a bunch of reasons. First, every airplane POH I've seen has specified that the oil must qualify to a standard - either MIL-L-6082 or MIL-L-22851 (though those have been superseded by an SAE standard). Modern automotive oil doesn't meet that standard, and therefore is effectively forbidden by the POH. More to the point, automotive oil is bad for aviation engines.

Aviation and automotive engines work on the same basic principles, but many of the details are different.1 One significant difference is that aviation engines normally burn some oil as they run, while well-performing automobile engines burn little or none.

Automotive oil contains a number of additives, such as detergents and wear inhibitors, intended for use where the oil doesn't burn off. Some of those additives do not burn completely, but instead stick around in the form of ash, where they can foul the engine and create deposits that lead to pre-ignition. That is why aviation oil is ashless dispersant: it cleans the engine by dispersing combustion byproducts into the oil (to be removed on the next oil change), while being ashless when burned. Lycoming considers it serious enough to put in an all-caps "CAUTION" section in their Lubricating Oil Recommendations document: 


  UNDER
  NO CIRCUMSTANCES SHOULD AUTOMOTIVE OIL BE USED. THE USE OF AUTOMOTIVE
  LUBRICANTS IN TEXTRON LYCOMING ENGINES IS NOT RECOMMENDED BECAUSE ITS
  USE COULD CAUSE ENGINE FAILURE. 


If all of that wasn't enough, use of an improper oil may void your engine warranty. In short: don't use it.

References:


An editorial summary on Avweb
An aircraft engine overhauler's best practices
Lycoming's Lubricating Oil Recommendations


1) Note that I'm referring to air-cooled aviation engines that burn 100LL - made by, say, Lycoming or Continental. Rotaxes and new aero-diesels are different, and more like their respective automotive counterparts; in fact, Thielert engines are actually based on automotive diesels.