A native of Toronto, Ontario, Brad May played Junior B with the Markham Selects before joining the OHL's Niagara Falls Thunder in 1988-89. May was one of the most imposing forwards in the league and was claimed 14th overall by the Buffalo Sabres at the 1990 NHL Entry Draft. A member of Canada's 1991 Gold Medal World Junior Team, May showed plenty of spunk as a rookie with the Sabres in 1991-92 with eleven goals and 309 penalty minutes. In 1992-93, May's defensive work improved and he scored the overtime winner in the first round playoff match up that eliminated the Boston Bruins.
The Sabres felt their young winger was on the way to becoming a more dominant figure after he scored 18 goals and reduced his time in the penalty box during the 1993-94 season. Injuries marred his year in 1994-95, but he rebounded with 44 points the next season and was a member of Canada's World Championship Team.
After parts of seven seasons in Buffalo, May was traded to the Vancouver Canucks in February 1998 and was a steady hard nosed player for them over the next two and a half seasons. In June 2000, he was acquired by the Phoenix Coyotes to add grit to their fast skating team. However, May's stay in Phoenix was short lived, after only two and a half seasons in Phoenix, the Vancouver Canucks re-acquired the feisty winger in hopes adding some grit to their roster.
May went on to play one full season with the Canucks before having his rights acquired by the Colorado Avalanche in the summer of 2005. As a member of the Avalanche, May would only suit up for 10 games before being dealt to the Anaheim Ducks at the 2007 NHL trading deadline for Michael Wall. The trade proved to be a blessing in disguise for Brad May. With him in the line-up, the Ducks went 7-2-4 and his physical presence led the Ducks to their first Stanley Cup championship.