Basically eh... 3 type I think...
Nigiri - The most common type where U got the sushi rice on the
bottom and the main item on top... May come with or without
seaweed... Common nigiri are: Salmon Sushi, Tamago Sushi, Kani
Sushi etc etc...
Maki - A circular roll which consist of sushi rice outer, then
main item in the inner... May or may not be wrap with
seaweed... Common maki are: California maki, Kani Maki, Tamago Maki
etc etc...
Temaki - A handroll... More in a cone shap with the rice and
main item inside...
There are of coz a few more types but those are
more uncommon... such as oshisushi, chirashi sushi(though U
still can find this type in places like sakea sushi)...