Former 1,500m world champion Cram has been made a CBE in recognition of his work as chair of the English Institute of Sport (EIS), and long-distance runner Sly an MBE for her services to athletics. Both won silvers at the 1984 Los Angeles Games.
Peters, who claimed gold in the pentathlon at the 1972 Olympics and was made a Dame in 2000, has now been made a member of the Order of the Companions of Honour for her work in the community.
Her Northern Irish compatriot Jim Boyce, who is the outgoing vice-president at FIFA, receives an OBE for services to football, as do former England & Wales Cricket Board chief executive David Collier and Cheltenham Festival pioneer Edward Gillespie.
There are also MBEs for Crewe Alexandra's long-serving chairman John Bowler, Portsmouth legend Linvoy Primus, Northern Irish boxer Paddy Barnes and England and Great Britain hockey captain Kate Richardson-Walsh.
Britain's Canadian skeleton coach Mark Wood is honoured with an MBE in the diplomatic and overseas list, while Sarah Hunter and Rochelle Clark - who were members of England's women's rugby team which lifted the World Cup in August, end a memorable year with MBEs.
Paul Murphy, a past chairman and president of the Rugby Football Union, receives the British Empire Medal, but rumours that World Cup winner Jonny Wilkinson would receive a knighthood have proven unfounded.