He played ten seasons in the National Hockey League (NHL) with the Ottawa Senators, New York Rangers, Phoenix Coyotes, Tampa Bay Lightning and the Nashville Predators.

He then played two seasons in Europe before retiring, with České Budějovice, and Elitserien team Södertälje SK.

Neckář played junior hockey with České Budějovice in 1991–92 followed by two seasons with their pro team.

He returned just in time to play two playoff games for the team en route to winning the Stanley Cup.

During the 2004–05 NHL lockout he played in his native Czech Republic, returning to České Budějovice.