Do they serve sushi on flights?

It's very common for airlines to offer sushi on flights to/from/within Japan, as well as for Japanese airlines on flights anywhere. However, most sushi served in coach is not the best quality (because typical coach meals are not the best quality, regardless of what they are). If you can use miles to upgrade to business class, the quality and variety of sushi (as for other meal items) will improve a lot. Longer-haul flights often have better food than short-haul ones, so a flight within Japan may not have as nice food as a flight between Japan and North America or Europe or Australia/New Zealand.

Sushi on flights to/from/within Japan is so common that there's no point in listing the airlines that offer it. My guess as to which airlines might not have sushi would be the very low-cost, no-frills ones.

When sushi is offered, it is usually done as one of the standard choices, not as a special meal 9which are usually for dietary restrictions), but may be pre-ordered at some airlines. If you want to know, usually the airline reservation desk can tell you. Just call, there shouldn't be a charge just to ask the question (only to issue or change a ticket).

For example, on American Airlines, sushi is the appetizer on the business class "summer meal" Japanese meal option. See Business Class Japan to U.S. - Summer Menu

From what I can find there is Sushi served on Asiana Airline but you can probably find it in other airlines as well just browse Airline Meals.

Or just a quick search for Sushi

I actually prefer to pick up sushi in the airport and then take it onto the plane. I fly with Delta and United most often and have never been served sushi, even in first class.

Airline meals tend to be either generic so as to be at least somewhat edible to as many people as possible or tailored to the destination or departure point, or tailored to the culture of the airline's home country (which of course often comes down to the same thing).
They're also designed to be easy and cheap to create and take well to freezing, microwaving, and long term storage.

Given that sushi is very much an acquired taste, expensive to make well, can't be frozen, and can't be stored long term after preparation, it's not going to be a popular meal choice with airline executives for serving their passengers except maybe on flights to and from Japan (and then likely mostly on shorter flights, and in business class or first class only).

Your best bet is to try to find a sushi bar at your departure airport and have a snack there before your flight, maybe they'll be able to pack you some for underway but with all the "security regulations" nowadays you might get in trouble for bringing food on board, and of course the wasabi or soy sauce would fall under the ban of liquids and gels.

Apparently KLM has just started their A la carte menu in Economy Class (currently only be ordered for KLM flights from Amsterdam to Abu Dhabi, Lima and Nairobi) and has a meal called "Japanese Delight" which does promise to serve sushi on intercontinental flights!