Nintendo is no stranger to making good games, and Mario's Galaxy has been considered one of the best examples for their impressive production rate (at least compared to Microsoft and Sony). The game isn't too different from other Mario games, but it does have some unique elements.
One of the more interesting features is the addition of Yoshi as a rideable mount for Mario. The alien-looking dinosaur acts as extra life number two and adds an entertaining way to explore levels. The graphics are also very pleasing on the eyes, with excellent 3D environments and a great use of colors.
Super Mario Brothers 2 (aka The Lost Levels)
The last game on this list is actually one of the best in the entire series, but for some reason it was under-appreciated upon its release, due to being released in different countries as "Super Mario Bros.: The Lost Levels" (a title that caused it to be overlooked).
This game is a bit different from the original Super Mario Brothers, but they're all good in their own way and this one changed the formula enough to stand out.
In this one, you'll have more enemies moving on screen at once and fewer opportunities for moments to catch your breath. The only odd thing about this game is that the falling platforms all have a different pattern of movement, unlike the first game.
Super Mario RPG: The Legend of the Seven Stars
This is one of my favorite games from childhood and it's still good even today, though replaying it now shows its age.
Game producer Shigeru Miyamoto (the man responsible for many Nintendo games, such as the original Mario Bros. and Donkey Kong) worked on this game along with battle system designer Akihiko Matsui and composer Yoko Shimomura (who was famous in the 90's for her work on Street Fighter 2: The Animated Movie Soundtrack).