I have 3 cars, none use any oil betweeen changes, I have sent the oil out for analysis after the 15000 mile changes and it is always still good...
One engine that shouldn't be fed synthetic is the Wankel (RX-8, RX-7, etc). Mazda has had an overwhelming number of cases of ruined apex seals that they've traced back to synthetic oil. This engine is desgined to 'burn' oil and synthetics are formulated to resist burnoff. A good quality conventional is best for this engine.