- 2002-11-26 • Traded to Florida Panthers by Los Angeles Kings with Andreas Lilja for Dmitri Yushkevich and NY Islanders' 5th round pick (previously acquired, Los Angeles selected Brady Murray) in 2003 NHL Entry Draft
- 2003-12-11 • Signed as a free agent by Avangard Omsk (Russia)
Jaroslav Bednář began his career with Slavia Prague in 1994 and stayed there for three years before moving to their rival team, Sparta Prague. He played just 14 games before moving to HC Plzeň and then returned to play for Sparta for the next season. He then spent the next two seasons playing in Finland's SM-liiga at JYP and HIFK where he led the teams in goals and points and finishing second overall in points in 2000-01.
Drafted by Los Angeles Kings in the 2001 NHL Entry Draft as 51st overall, he moved to North America and was supposed to be key offensive player for the Kings. However, he was never able to recapture the form he had in Finland. Bednář spent the majority of his first season with the Kings AHL affiliate in Manchester tying for fifth in team goal scoring with 16 while playing in 22 games with the NHL team. On November 26, 2002, Bednář, along with Andreas Lilja was traded to the Florida Panthers for Dmitri Yushkevich, he played 65 games for Florida, scoring 6 goals and 14 assists for 20 points.
He started the next season in Florida, but being given less opportunity, he decided to return to Europe, signing Avangard Omsk in Russia. He helped the team to win the title in 2003-04 and stayed there the following season.
In 2005, Bednář returned to Slavia Prague where he has become one of their core players, winning Czech champion title in 2007-08 and left the team after four years on April 29, 2009 to sign with Torpedo Nizhny Novgorod of the KHL. The next three seasons he settled in Switzerland, playing for HC Davos, HC Lugano and SC Bern with brief appearance back in HC Slavia Prague. During his time in Switzerland he won two titles, with Davos and Bern.
After that, he returned to HC Slavia Prague for the fourth time and still belonging to one of the top scorers in the league. Before 2015-16 season he left his original club and signed with HK Hradec Kralove.
Bednář represented Czech republic on two World Championships (2006, 2007), winning silver medal in 2006.