Born in Celadna, Czechoslovakia, Pavel Kubina spent four years with the junior and senior teams of the TJ Vitkovice club. He was chosen 179th overall by Tampa Bay in 1996 when he was still in Europe. Kubina decided to play the 1996-97 season with the WHL's Moose Jaw Canucks to become more acclimatized to the North American game. The Lightning were encouraged when he led his club's defence with 44 points in 61 games and registered 116 minutes in penalties.
Kubina played most of the 1997-98 schedule in the AHL with the Adirondack Red Wings but also showed flashes of his potential in ten games with the Lightning. The talented rearguard recorded 21 points in 68 games for Lightning in 1998-99. He ranked first among NHL rookies in average ice time per game (22:47) and third in hits (156). Following the regular season he helped the Czech Republic win the gold medal at the World Championships in Norway and finished second among defencemen with eight points.
Kubina continued his improved play in 1999-00 by leading the Lightning in power-play goals and providing a physical presence on the blueline. He set a personal high with eleven goals in 2000-01 to rank fifth on the Lightning and for the second time in his career represented the Czech Republic at the World Championships.
In 2001-02, Kubina established a career high in assists with 23 and points with 34 before representing his country in February at the Winter Olympics in Salt Lake City and later that spring at the World Championship. After coming off a career year in points, Kubina's offensive numbers dipped in 2002-03, however he remained one of the team's most durable players as the Lightning entered the post season for the first time since the 1995-96 season.
Coming off a second round elimination in the 2003 playoffs, Kubina and the Lightning rebounded in 2003-04 capturing their first Stanley Cup title in franchise history.
In the fall of 2004, Kubina represented his homeland at the World Cup of Hockey and in the spring of 2005 captured Gold at the World Championship.
In the summer of 2006 Kubina became an unrestricted free agent and was signed by the Toronto Maple Leafs. Earlier that year, Kubina represented his homeland at the 2006 Winter Olympics and earned a Bronze medal.
Despite three solid seasons in Toronto, trade rumours dogged Kubina throughout his time with the Maple Leafs. It was even reported that he exercised his no-trade-clause to nix a potential deal with the San Jose Sharks at the 2008 NHL trade deadline.
In the summer of 2009, with the Maple Leafs again missing out on post-season play, Kubina's no-trade-claus was void and the writing appeared to be on the wall for the big defenseman. Talks that he would be traded heated up. Finally, on July 1, 2009, it was announced that Kubina had been traded to the Atlanta Thrashers along with Tim Stapleton for Garnet Exelby and Colin Stuart.
In the summer of 2010, the big defenseman was again an unrestricted free agent and this time inked a 2-year deal with the club where his NHL career began, the Tampa bay Lightning.
In the days leading up to the 2012 NHL trade deadline, Kubina was traded to the Philadelphia Flyers in exchange for Jon Kalinski and a package of draft picks.