I'll probably not remember if the 'cartoon' I watched was an anime at all, but I guess the safest guess is Sailor Moon. I seem to have memories of catching a glimpse of it or something. I didn't watch an entire episode, just a minute or two, but that's probably the first anime I came across.
The next best guess would be Pokemon... Then Dragonball. After that came the more recent animes- meaning, present a few years back, less than a decade, in short.
The next best guess would be Pokemon... Then Dragonball. After that came the more recent animes- meaning, present a few years back, less than a decade, in short.