Kölliker began his pro career in 1972 with EHC Biel in the Nationalliga B. Soon an essential member of the team, he helped the team promote to the Nationalliga A in 1975-76. He was thrice NLA champion with EHC Biel in 1978, 1981 and 1983. He stayed with Biel until 1985-86 NLA season|1985-86, when he joined HC Ambri-Piotta. He played four seasons with Ambri-Piotta before returning to his old team, Biel, and retiring three years later, in 1993.
When his playing days were over, Kölliker turned to coaching. He coached his former team, EHC Biel, then SC Langnau. He also coached the Swiss U20 team and since 2007, he is assistant coach with the senior team.
- Swiss champion: (3) 1978, 1981, 1983
- International Ice Hockey Federation Hall of Fame induction: 2007
- World Championship All-Star team nomination: 1980