The knife can be seen and used a fair number of times, most notably in the missions Sarah and Election Campaign. In the former mission, some of the hooligans use the knife, and it can be looted from their bodies or picked up if they drop it. The same applies to the criminals in the old jail. It should be noted that only the first group you encounter uses melee weapons. Also, at the Corleone Hotel, there is a knife in one of the rooms on the first floor.
You can find more real world information about the knife on its Wikipedia page.