There are a few different kinds, depending on how the item is presented. They are:
Usually a bowl or box of sushi rice topped with a variety of sashimi.

Aburage (fried pouches of tofu) stuffed with sushi rice.

The rice and seaweed rolls with fish and/or vegetables. There are also more specific terms for the rolls depending on the style. They are Futomaki(Thick Rolls), Hosomaki(Thin Rolls), Uramaki(Inside- out Rolls)

The little fingers of rice topped with wasabi and a filet of raw or cooked fish or shellfish. Generally the most common form of sushi you will see.

Also called a hand-roll. Cones of sushi rice, fish and vegetables wrapped in seaweed. It is very similar to maki.

Beginning as a method of preserving fish centuries ago, sushi has evolved into an artful, unique dining experience. In its earliest form, dried fish was placed between two pieces of vinegared rice as a way of making it last. The nori (seaweed) was added later as a way to keep one's fingers from getting sticky.

Sashimi is raw fish served sliced, but as-is. That means no rice bed or roll, but it is often served alongside daikon and/or shiso. This is my favorite style as you really get the flavor of the fish. Plus, it's a great way to impress sushi newbies!
Depending on what you ordered and the whim of the chef, you might see items such as wasabi (the hot green Japanese horseradish-like rhizome).
Gari (pickled ginger, which comes in both a pink and a light tan color, with the lighter stuff usually indicating better quality).
You may also see a large green leaf called shiso, which is often served with sashimi, and a shredded white mass of Japanese radish called daikon, which is also often served with sashimi.