Career
During his career he played for Brigg Town, Hull City, Boston United, Burton Albion, York City, Gainsborough Trinity and North Ferriby United. Hull City
He spent his whole Hull career playing in the Third Division and made 204 appearances and scored 12 goals in all competitions before being released in 2002. Boston United
He was signed by Boston United caretaker manager Neil Thompson in August 2002.
He signed a new two-year contract with the club in April 2004 and after this expired he agreed to a one-year deal in May 2006.
Burton Albion
He made 46 appearances and scored five goals in the 2007-2008 season but missed the play-offs due to a broken jaw. York City
He was released after a season at Burton and joined fellow Conference Premier side York City on 14 May 2008.
He was appointed as club captain for the 2008-2009 season. His debut came in a 1–0 victory against Crawley Town and scored the only goal in the subsequent game against Wrexham.
Greaves suffered from foodborne illness in September, which resulted in him losing 9 pounds, and missing York"s match against Kidderminster Harriers.
He started in the 2009 FA Trophy Final at Wembley Stadium on 9 May 2009, which York lost 2–0 to Stevenage Borough. Following the end of the season, during which he made 46 appearances and scored four goals, he entered negotiations with York over a new contract. Gainsborough Trinity
Greaves was eventually released by York in June and signed for Conference North team Gainsborough Trinity on 7 July.
He made 37 appearances and scored one goal in the 2009-2010 season and he signed a new contract with the club in June 2010.
North Ferriby United
Greaves was among a number of players released by Gainsborough at the end of the 2010-2011 season and on 28 June 2011 he signed for Northern Premier League Premier Division side North Ferriby United. In October, having made 11 appearances in all competitions for North Ferriby, Greaves announced his retirement as a football player.
Hull United
On 30 January 2015, he returned to the game, joining Humber Premier League outfit Hull United.