Saw is a movie franchise that relies heavily on the gore factor in order to keep the audience shocked and/or titilated. Other such ones include Hostel, Chainsaw Massacre and The Hills have eyes.
While the original Saw was a shocking modern classic in it's own right the subsequent sequels have diminished it's originality and reduced the public perception to shock gore.
So, saw is a subgenre of the horror genre. Just not a particularly engaging one for people like myself.
Personally, psychological/zombie/supernatural horror are much more favoured by myself. Ie - The Ring and the 1st half of Dawn of the Dead remake.