Allison was born in North York, Ontario, but grew up in Toronto, Ontario.
Allison attended Humber Summit Middle School and Westview in Toronto, Ontario. His brother Todd attended the same schools. He played AAA Hockey with the Toronto Red Wings Hockey Club.
Allison was drafted 17th overall in the 1993 NHL Entry Draft by the Washington Capitals, amidst a stellar junior career for the London Knights of the Ontario Hockey League (OHL).
Allison played parts of two seasons with the Los Angeles Kings where, for a brief time, he teamed with former stars Žigmund Pálffy and Adam Deadmarsh. He has also played for the Boston Bruins and Washington Capitals. His best season was 2000–01 when he had 95 points. Allison has played 552 games in his career, racking up 154 goals and 331 assists for 485 points. He also has 25 points in 25 career playoff games. Allison missed most of the 2002–03 season and all of the following season because of a neck injury and concussion.
Prior to the 2005–06 season, Allison signed a one-year contract with the Toronto Maple Leafs worth $1.5 million, with bonus incentives for good performance. Allison suffered a hand injury in a game against the Montreal Canadiens, and had to have surgery on his hand, which sidelined him for the remainder of the season. In the 66 games he played in before the injury, he scored 17 goals and had 60 points for the Maple Leafs.
After the 2005–06 season, Allison became an unrestricted free agent. Toronto chose not to re-sign Allison because new head coach Paul Maurice and GM John Ferguson, Jr. did not feel he would be a proper fit for their new, young, fast-paced team.
Allison subsequently did not sign with a team for the 2006–07 NHL season, despite rumours of multiple contract offers. In retirement Allison operated a horse farm north of Toronto.
On August 28, 2009, Allison received an invitation to the Toronto Maple Leafs September 2009 Training Camp and trained with them through the beginning of the preseason. Allison had not played professionally since 2005–06; in explaining the invitation, Brian Burke, the general manager of the Maple Leafs, said: "He had some personal issues and some major physical issues at that time. He has solved all of those. In my mind, he is a guy who might give us a lift and he deserves that opportunity,"
In an interview after his first exhibition game back, Allison was as confident as ever. "I didn't contribute much, but that's to be expected, I'm just shaking the cobwebs off. I fully anticipate regaining my previous form as a point per game player."
Allison's bid to make the team on a tryout ended up falling short. The training invite yielded a memorable moment, when Allison fought with the Philadelphia Flyers' Darroll Powe during an exhibition game and ripped his helmet in half with his bare hands. It was not enough, however, and by September 28, Maple Leafs head coach Ron Wilson confessed that Allison was "out of the plans."