You shouldn't need it for Settlers 3 if I'm not mistaken. If you're asked for it, try simply restarting.

same problem here. pls help

Same solution. Just restart it.

A bit late:

Use your web browser and not GOG Galaxy and you can find it under the more button.

Not for Settlers 3. For this game, you just restart.

But there is a key. I didn't need it but I can find it under more. Perhaps for multiplayer.

Ah, ok then. Maybe some previous version need it for single player and they're still providing them. Or as you say, multiplayer.

no, this is a bug and its been there since the first release of settlers 3 on gog.

Yeah I just had this same issue. Had to log in through my web browser and key was under 'More' like you said. Many thanks!

Nope - it is not a bug. You really need it for multiplayer together with the s3_multi.exe.

yes it is... at first start it pops up, but never again after that, if you type it in or not. so i guess its supposed to register automatically but just doesnt on first start. if you really need the key for multiplayer, why would the game only give you the option to type it in once and never again after that? makes no sense at all

Nope - you are mixing here two things:
1. It is a bug if the game asks you for the key when you start it using the single.exe - as then the game should use a hard coded CD Key which is the same for every user.
2. It is not a bug if the game asks you for the CD-Key when you start it using the S3_multi.exe - because it doesn't use then the hard coded CD-Key, so you can play with other users (==keys). Simple as that.

so I was so annoyed with this settlers 3 ultimate asking for the serial number upon install non-drm and I restarted, it didn't work.
BUT I uninstalled it and then reinstalled it and WHAT DO YOU KNOW, the serial number request just disappeared.