Ok, I just bought a new system, I downloaded GOG launcher, The n started downloading my games. When The first game was finished (Morrowind) I started it but my saved games are not there. Is this normal? Please help.

Yes, it's normal; you downloaded the game (which is the same for everyone), not the saves (which are not). If you want those saves, you need to copy them from the previous computer that has them.

(The only exceptions are games that support cloud saves, and only if that feature is enabled.)

Thank you for your quick reply, what is that folder called and how do I get into the right place?

Try this

Computer/Local Disc (C:)/Users/[your username here]/AppData/Local/Virtual Store/Program Files (x86)/Bethesda Softworks/Morrowind/Saves
and make sure you can see hidden files

You can simplfy your search for appdata by using the Windows macro variable:
%appdata%

Put that exactly into windows explorer and it will take you there.

%appdata% will take you to AppData\Roaming, to go to AppData\Local use the %localappdata% variable.

True. There are quite a few others if anyone is interested:
https://technet.microsoft.com/en-us/library/cc749104%28v=ws.10%29.aspx?f=255&MSPPError=-2147217396

Check pcgamingwiki for any game you want. You find there info about save game location, settings, patches, bugs and lots of other things.