Palffy entered big league hockey with AC Nitra, which at the time was the weakest team in the joint Czech-Slovak league. As a 19 year-old youth, he scored 34 goals. It was also where he played for the first time on right wing next to Josef Stumpel. He also played with Stumpel for the junior national team.
Palffy then left for Dukla Trencin and together with Robert Petrovicky and Branislav Janos created the most feared offense in top-level competition. In the 1991-92 season, he became the best shooter and most productive player with 41 goals and 74 points in 45 games. At the same time, he helped Trencin win the country's title.
In 1991 he took part in the World Junior Championship and he made his debut with the Czech senior team in the Canada Cup. However, a shoulder injury prevented him from taking part in the 1992 Olympics. The New York Islanders drafted him in the summer of 1991 in the second round. In the 1992-93 season, his last in competition in his home country, he collected 79 points in 43 games and once again ascended the throne as the most successful points collector.
After his arrival on Long Island, he took number 68 made famous by Jaromir Jagr. But when he started his professional career in 1993, he didn't become a top-notch player right away. He couldn't speak a word of English and was getting used to a new lifestyle and a new style of playing hockey. The better part of the following two seasons were spent with the Salt Lake City Golden Eagles and the Denver Grizzlies of the IHL. He even got the chance to play for Slovakia when the country made its first independent appearance in elite competition during the 1994 Lillehammer Olympics.
In the 1998-99 season, he got a late start because he and the Islanders couldn't agree on a new contract. Before the dispute was settled, he played at home in Skalica and in eight games gave his home team 11 goals and 19 points. After his return to Long Island, he kept earning a point a game. However, his teammates were leaving the team one by one. In the summer it was Palffy's turn.
In the summer of 1999, the Los Angeles Kings acquired Bryan Smolinski and Palffy for a pretty high price, young players Olli Jokinen, Josh Green, Mathieu Biron and the first choice in the next draft. On the new team, he once again met with his old acquaintance Josef Stumpel and together with Luc Robitaille they created a powerful new line.
Upon his arrival in Los Angeles, Palffy quickly became a fan favourite and became one of the premier players in the league. However, the talented Slovak found himself signing with the Pittsburgh Penguins in the summer of 2005 once the NHL lock out season came to an end.
Palffy went on to play 42 games with the Penguins before abruptly announcing his retirement from the game on January 18, 2006 due to recurring shoulder injury. Throughout his playing career, the Slovak native registered 713 points (329-384-713) in 684 NHL games.
Throughout his playing career, Palffy has been a foot soldier when called upon to represent his country, which includes; World Junior Championship (1991-1992), Canada Cup (1991), World Cup of Hockey (1996 and 2004), Winter Olympics (1994 and 2002) and World Championships (1996, 1999, 2003, 2004, 2005).