2006-07: Greg Burke played in 34 games for the New Hampshire Junior Monarchs in the ECHL and scored 6 goals with 12 assists and 22 PIM in 34 games. Burke was selected by the Cedar Rapids Rough Riders of the USHL in the second round (4th overall) of the USHL Futures Draft.
2007-08: Burke led the New Hampshire Junior Monarchs in scoring with 21 goals and 25 assists with 46 PIM in 40 games. He committed to playing college hockey in 2009-10 for the University of New Hampshire.
2008-09: Burke played for the United States at the World U-17 Challenge but played just eight games with Cedar Rapids in the USHL before suffering a season-ending shoulder injury. He finished the season with 2 goals and was -1 with 8 PIM.
2009-10: Burke played in 32 games as a freshman at New Hampshire. He scored his first collegiate goal in a 5-2 win over Vermont on December 6 and finished the season with 2 goals and 8 assists. For the year, he was -8 with 18 PIM. The season came to a disappointing end for the Wildcats, who won the Hockey East regular season title. In the Hockey East best-of-three quarterfinals, New Hampshire won the opening game against Vermont, 7-4, but was then shut-out in back-to-back 1-0 games – the second one in OT. In the NCAA East regional, New Hampshire dumped ECACHL champ Cornell, 6-2, with Burke assisting on two goals, but then fell to Atlantic Hockey's RIT, 6-2, missing out on a trip to the Frozen Four.
2010-11: Burke had a difficult sophomore season for the University of New Hampshire – missing time due to a shoulder injury and a case of mononucleosis. Burke skated in 18 games for the Wildcats; scoring 2 goals with 1 assist and was an even plus/minus with 12 PMs. The Wildcats finished second in Hockey East and advanced to the NCAA Northeast Regional Final.
2011-12: Burke appeared in a career-high 34 games in his junior season at New Hampshire. Playing both center and wing, he scored 6 goals with 5 assists and was -11 with 36 penalty minutes. Three of his six goals were scored on the power play. The Wildcats finished sixth in Hockey East in a rare losing season and lost to Boston University in an epic quarterfinal series that included two double overtime games.
2012-13: Burke skated in 13 games for New Hampshire in his senior season, suffering a season-ending shoulder injury in January after dealing with a concussion. He scored 3 goals with 2 assists and was +1 with 21 penalty minutes. The Wildcats finished in a three-way tie for third in Hockey East but received an at-large bid to the NCAA tournament after losing to Providence in a three-game Hockey East quarterfinal series. UNH defeated Denver before falling to Massachusetts-Lowell in the NCAA Northeast Regional final.
Burke has added weight to his once-lanky frame and is a big player with above average offensive skills and a fluid skating stride for someone so tall. Burke missed most of the 2008-09 season due to shoulder surgery but the injury allowed him to train and develop strength in preparation for college hockey. Burke is still a long-term project in terms of development but has the prototypical size and skating ability of a power forward with some scoring touch and a desire to improve. He should benefit from the extra developmental time of a college career and could be an intriguing prospect in two or three years.
Burke was not tendered a contract by the Washington Capitals prior to the 2013-14 season, and is not currently playing pro hockey.