There are two different types of DVI ports: DVI-I or DVI-D. DVI-I carries digital and analogue signals, DVI-D just digital signals.
You can connect any single-link DVI cable (DVI-I as well as DVI-D) to a dual-link DVI-I port. You can also connect a single-link DVI-D cable to a dual-link DVI-D port.
However, you cannot connect a single-link DVI-I cable to a dual-link DVI-D port.