Over the years, manufacturers have changed where this information is located on an outboard. I'll try to be as complete as possible below, while keeping this reasonably simple.
On older Mercury outboards, going back into the 50's and possibly even earlier, the serial number would generally be viewed at the leading edge of the swivel bracket, as seen in the image below. If for any reason that number may have been changed, removed, or can no longer be read, every Mercury had a freeze plug, which is on the powerhead and about the size of a quarter. That freeze plug will have a serial number on it. So long as you know your HP and the serial number, you can identify the year of your outboard.
On later model Mercury engines, the serial number was located on the swivel bracket, as shown in the picture below. First, these would be on a metal tag and stamped with the numbers. Later, the numbers were printed on a vinyl tag. Unfortunately, you'll often find that the vinyl tag has washed out. If you can no longer read the number on the tag, you’ll want to find that freeze plug on the powerhead in order to identify the outboard.
Johnson & Evinrude
Johnson and Evinrude outboards both work with model numbers for identification. In most cases, the model number is located on either the transom or swivel bracket. It can usually be found on a either a metal plate on earlier models or a sticker on later models. Once they switched over to the tags, this was another number that often washed out and could no longer be read. In this case, the powerhead freeze plug can be located and will have the serial number. The serial number itself won't do you much good, but an authorized dealer can use the serial number to match the engine up with a model number again.
Chrysler outboards work by a model number. There are 2 locations where you may find this number. Early Chrysler models stamped it on a metal plate and it was placed under the carburetors, inside the lower cowling, or pan. Later models used the same plate, but you'd find it on the side of the transom bracket.
Force outboards used model numbers on vinyl tags, many of which washed out. If the number washed out, you may find a small sticker either on the cylinder head cover or the starter bracket. If that fails, all is not lost. There are numbers stamped on your carburetor. Take those numbers and google them or email us. Those numbers will usually nail down a year and HP for your engine.
Nissan, Tohatsu, Suzuki, Yamaha, and Yamaha Mariner use both model and serial number information. That tag can almost always be found on the side of your transom bracket, as shown below.