The career path for aspiring Gordon Gekkos is getting rockier.

Goldman Sachs Group Inc. is doing away with two-year contracts for most analysts hired out of college, according to communications reviewed by The Wall Street Journal and confirmed by a Goldman spokesman. Analysts also won't get bonuses for completing the program, which has been around for a quarter of a century and has been viewed as a meal ticket to a lucrative Wall Street career.

Goldman's...