According to Howstuffworks.com, there may be a few instances where an engine flush is required, but engine technology has developed to the point where engine flushes are not needed and in fact may be harmful to the engine. Also, according to NBC news, Honda and other major car-makers have issued memos to mechanics advising that after engine flushes, there is a high incidence of damage to the engine's interior.
During an engine flush, chemicals are poured into the engine after the old oil has been removed and the engine is idled for a few minutes to dissolve oil deposits and sludge. Then, the chemical is drained and fresh new oil is put in. This is usually done on vehicles where the maintenance records are not known or on vehicles where the oil has not been changed regularly, as following regular maintenance schedules keep the engine oil fresh, and one of the functions of motor oil is to clean and remove old oil deposits and sludge. During an engine flush the same deposits that get broken and dissolved by the chemicals can migrate to other parts of the engine, clogging them and causing extensive damage. This damage is also not covered in any car manufacturer's warranty.