Sushi is served in all kinds of shapes and sizes:
Nigiri
This is the most traditional style, which is simply fish on rice. This or sashimi is the best choice for fully experiencing the taste of rare or high-quality fish.
Sashimi
Also a very traditional style, which is simply cuts of fish. Oftentimes, it is ordered as a platter with a variety of fish and is typically eaten with rice on the side as well.
Rolls / Maki / Uramaki
In this style, nori (seaweed) is used to roll fish and other ingredients such as vegetables with rice. The rice may either be inside the roll (maki) or outside (uramaki). Furthermore, they may be topped with additional items such as fish, avocado, sesame seeds, and even various sauces. While the more exotic rolls aren't very traditional, they are delicious and extremely popular in the U.S. Generally, restaurants offer various combinations of choices both inside and outside the rolls even including fried items in some cases.
Hand rolls / Temaki
The hand roll, or temaki, is similar to (ura)maki rolls, except that it is cone-shaped and is meant to be served in one piece. In some cases, the nori taste may be more prominent, so that can change the flavor. Otherwise, it is very similar to rolls but may offer a slightly different eating experience.