A veteran of 1,260 NHL games, Radek has played for the Panthers, New York Rangers, Edmonton Oilers, St. Louis Blues, Atlanta Thrashers, Dallas Stars, Anaheim Ducks and the Carolina Hurricanes.

In 77 games, Dvořák scored 13 goals and 27 points, as the Panthers reached the playoffs for the first time in club history.

In 2000–01, Dvořák was placed on a line with fellow Czechs Petr Nedvěd and Jan Hlavac and he would have a breakout season.

On March 11, 2003, the Rangers traded Dvořák and Cory Cross to the Edmonton Oilers in exchange for Anson Carter and Aleš Píša.

Dvořák returned to the Oilers in 2003–04, where he scored 15 goals and 50 points in 78 games, however, Edmonton failed to make the playoffs.

In the playoffs, Dvořák had two assists in 16 games, as the Oilers lost to the Carolina Hurricanes in the 2006 Stanley Cup Finals.

The Blues failed to qualify for the playoffs, and Dvořák left as a free agent after the season, returning to the Florida Panthers on July 1, 2007.

On February 28, 2011, the Panthers traded Dvořák (along with a fifth-round pick in the 2011 NHL Entry Draft) to the Atlanta Thrashers in exchange for Patrick Rissmiller and Niclas Bergfors.

During the 2012–13 NHL lockout, and as a free agent, Dvořák signed a contract with HC Davos of the Swiss National League A.