Earth Defense Force
Illusion of Gaia
One of my favorite SNES action RPGs is also a fairly short one. The graphics are top-notch and the music is also catchy. If you like Ys or Zelda, try this classic. It is best to play this one in short bursts, but if you have one whole day to relax, you could certainly find worse ways to kill time.
Mega Man X
Cybernator is for people that love awesome 2-D action and robots. If you fall into this cateogory (and who doesn't) then play this game. It has not been re-released on a virtual service, which is unfortunate, but track it down for a rainy day by legal or shady means. You will not be disappointed. This one also has a fan-made patch that re-implements the Japanese character art and infamous suicide scene for those interested in seeing the original version fully intact.
Violinist of Hameln
http://superfamicom.org/translations/info/violinist-of-hameln-english) so now you can enjoy the story.