Moomin Tanoshii no Ikka. <3 It was an anime based on the children's book series by Swedish-Finnish author Tove Jansson. Basically everyone in Finland has watched it.
As for more not "Finland-only" series... Pokémon, Digimon, Dragonball Z, Sailor Moon, Magic Knights Rayearth... can't remember which I saw first, all were broadcasted around the same time. ^^''