What type of computers are in a flight system?
Historically, avionics manufacturers have used off-the-shelf processors on custom circuit cards.  Processor selection has been based on getting a reliable processor (established history) at a reasonable price and an expectation that it will be available for a long time.  The high turnover (obsolescence) in processor design along with a lack of design integrity in commercial products is causing avionics companies to move towards custom chips.  Though some products meet the integrity by using two dissimilar processors (though it doesn't address the obsolescence issue).  I am aware of a number of older designs using 486 and PowerPC processors.  

Operating systems (just like all the a/c software) have to comply with the appropriate level of DO-178 (currently rev C).  In practical terms, that means the OS has to meet DO-178 Level A.  There are a number of commercial solutions available.  LynxOS-178 is one.  Integrity-178 is available from Green Hills.  Wind River also has a product available.