Of all the different types of sushi, the one that we can say with certainty is gluten-free is sashimi. It's naturally gluten-free, as there are no other ingredients than fresh fish. Sushi is the main course in most sushi stores, of course. It's basically rice, fish and vegetables.
However, you shouldn't use soy sauce because it's wheat; unless it's gluten-free soy sauce. Common sushi ingredients, such as rice, fish, seaweed, and vegetables, are gluten-free. Not all sushi is gluten-free. Sushi containing surimi (fake crab meat), tempura, or anything made with soy sauce or a marinade is not safe in the gluten-free diet.
It's also possible that the wasabi and vinegar used to make sushi rice contain gluten. Some sushi are gluten-free, while others don't. Sushi is a Japanese dish that is prepared with rice and fish with vinegar, other seafood, vegetables and even some fruits. You can buy real wasabi root powder at Asian grocery stores or order it online; Sushi Sonic and Pacific Farms are two manufacturers.
You can find sushi restaurants that serve gluten-free sushi, but if you're gluten-free and don't know what questions to ask, you could be putting your health at risk. As I learned the ins and outs of my new diet and became disconnected a little after a bad reaction at a new restaurant, I rarely ate sushi for a while. Sushi restaurants and their menus can be difficult to navigate, and there is often a language barrier when trying to explain the precautions you need to the sushi chef. Most sushi rice dishes are gluten-free, but you should ask the restaurant to read the label of the vinegar you used.
California rolls, by definition, unless you visit a high-end sushi restaurant, contain imitation crab. From a gluten-cross contamination standpoint, sushi restaurants are quite safe, you can sit at the sushi bar and watch the chef prepare your food, and unless the restaurant prepares tons of sushi in tempura, the sushi prep area is generally gluten-free except for soy sauce. If you like sushi as much as my family does, you'll want to dine at a sushi restaurant sometime. Don't include sauces on top of or inside your sushi rolls, unless the waiter checks the ingredients.
In addition, imitation crab, also called surimi, found in many rolls such as those in California, is made from fish and a food starch, which often contains wheat and, therefore, gluten. It's harder to get safe sushi in a supermarket sushi bar, but keep in mind that Wegmans supermarkets have made all their sushi gluten-free. However, there is a wide variety of sushi available, and some types include ingredients that are not suitable for people on a gluten-free diet. Many sushi restaurants (especially in the United States) don't use real wasabi; instead, they use a mixture of horseradish, mustard, and other ingredients (including green food coloring).
Don't risk eating surimi unless you know for sure that the sushi restaurant has experience in offering gluten-free sushi.