After parts of four seasons with Montreal, he was traded to the New York Islanders on June 22, 2002, along with a 2002 5th round draft pick for Mariusz Czerkawski.

As a free agent that summer, Asham left the Flyers and signed a one-year contract worth $700,000 with the Pittsburgh Penguins on August 20, 2010.

On May 13, 2013, he scored the series-winning goal in Game 7 of the 2013 Stanley Cup playoffs to push the Rangers into the second round and eliminate the Washington Capitals.

The Rangers did not offer to extend Asham's contract and on July 1, 2014, he became an unrestricted free agent, effectively ending his professional career.

In September 2015, Asham signed an amateur playing contract with the Gander Flyers of the Central West Senior Hockey League.

[6] Asham also has his own charity called "Arron's Chance to Play Hockey" (chance2play.com)[7] This foundation's mission is to work in partnership with the community to provide opportunities that will enhance the emotional, physical, social and intellectual well-being of children.