Kasparaitis left Lithuania for Russia at age 14 after training with Aleksey Nikiforov to play ice hockey at a higher level. Kasparaitis played his first game for Dynamo Moscow, one of the premier teams in the Soviet Union, at the age of 16 during the 1988–89 season, and won the Soviet League championship with them in 1992. He was drafted by the New York Islanders with the fifth overall pick in the first round of the 1992 NHL Entry Draft. Kasparaitis played for the New York Islanders, Pittsburgh Penguins, Colorado Avalanche, and New York Rangers.

Kasparaitis was known for his aggressive physical playing style and led his teams in hits several times, including his rookie season, in 1992–93 NHL season with the New York Islanders. On November 17, 1996, Kasparaitis was traded to the Pittsburgh Penguins. While playing for the Pittsburgh Penguins in 1998 Kasparaitis’ made a hard hit on Eric Lindros that knocked Lindros out of action for 18 games. On March 19, 2002, he was traded to the Colorado Avalanche at the trade deadline, where he spent the remainder of the 2001–02 NHL season. Kasparaitis eventually wound up with the New York Rangers when he was signed on July 2, 2002. During the 2005–06 season, he served as an alternate captain of the Rangers, along with Jaromír Jágr and Steve Rucchin, as the Rangers had no captain.

Because the Lithuanian ice hockey team was relatively weak and hadn’t ever played in major competitions, Kasparaitis chose to represent Russia in official events. In December 2005, Kasparaitis was chosen to represent Russia in the 2006 Winter Olympics in Turin, Italy. At the start of the 2006–07 season, Kasparaitis was replaced as an alternate captain with the Rangers by newly acquired Brendan Shanahan. He was waived by the New York Rangers on January 24, 2007 and subsequently demoted to the Rangers’ affiliate in Hartford.

Kasparaitis holds dual Lithuanian and United States citizenship. He is the father of six children. He has a daughter by his first wife, Irina. His second marriage, to Ingela ended in divorce in 2006. He and his current wife, Lisa, have twin daughters and three sons.

Kasparaitis was once again waived by the Rangers prior to the 2007–08 season. On November 3, 2007, the Rangers announced that Kasparaitis had been loaned to SKA St. Petersburg of the then-Russian Superleague (RSL), now the KHL. The deal was made possible due to a lack of a transfer agreement between Russia and North America at the time. However, the Rangers retained his NHL rights.

On June 19, 2010, Kasparaitis signed as the assistant coach for SKA Saint Petersburg of the Kontinental Hockey League (KHL). The contract expired on December 22, 2010.

In early 2015, Kasparaitis co-founded the Verzasca Group, a Florida-based real estate development company, of which he holds the title as president. They took the name Verzasca from the Swiss river, because of the “transparency that the firm strives to bring to both its investors and its development partners.” Later in the year, the company had gained approval on two residential projects in the Miami area.

In the 2009–10 season, he did not play due to an injury and eventually announced his retirement at the conclusion of the season. Since his retirement he has attempted to become eligible to represent Lithuania internationally, which he finally did in 2018, playing for the team in the World Ice Hockey Championships Division 1B.