Try 4 and 6, both are on SNES.
You'll have to be careful about IV though, because in the US it was released as Final Fantasy II, but they later released Japan's Final Fantasy II in the US, and called that Final Fantasy II, and properly started calling re-releases of II as Final Fantasy IV (like the DS version). To make sure you're playing the right one, you should start off as a knight named Cecil.
VI won't cause any issues, since it was VI in Japan and the US, but to be sure, you start off as a character named Terra.
Edit: Oh, I see you were asking for games OTHER than the FF series. In that case the obvious recommendation is Chrono Trigger, but also give Earthbound a try.