After you have a Chef knife you start to realize that as good as they are, they are not the ideal knife for everything. The other knives you should consider having on your toolbox:
Nakiri: a vegetable knife with a straight blade used for cutting vegetables.
Deba: a heavy knife used for filleting fish and cutting meat.
Yanagiba: a slicing knife used for slicing sashimi.
Honesuki: a boning knife used for separating meat from bones.
Takobiki: a slicing knife used for slicing raw fish.
Kiritsuke: a multi-purpose knife with a blade that resembles both a gyuto and a yanagiba.