Donkey Kong & Mario Bros., Arcade:

Mario made his first appearance in the game Donkey Kong. He was trying to save his girlfriend Pauline from the ape Donkey Kong. In Mario Bros., we are introduced to Mario's brother Luigi. The two of them go to investigate the sewers of New York, as there have been monster sightings.

Super Mario Bros., NES:

By far, the best selling Mario game ever. Super Mario Bros. has sold over 40 million copies. Mario and Luigi set off into the Mushroom Kingdom's 8 worlds to rescue Princess Toadstool (Princess Peach) from the evil clutches of King Bowser. Here we are introduced to many characters that are still with the Mario Bros. series today. We are introduced to Princess Peach, Bowser, Goomba, Koopa Troopa, and Toad.

Super Mario Bros. 2, NES:

In this adventure, we are introduced to Princess Daisy. Mario, Luigi, Princess Peach, and Toad are playable characters in this game, as Princess Daisy is the damsel in distress. The four heroes are traveling across Easter Island to get to Princess Daisy, only to have Mario wake up. That's right. A whole adventure, in a dream.

Super Mario Land, Gameboy:

Mario travels to Princess Daisy's home Sarasaland, to rescue her from the alien Tatanga. There are four areas to Sarasaland, and Mario has to travel through all of them to finally corner Tatanga in the skies of the Chai Kingdom.

Super Mario World, SNES:

Mario decides to take a well deserved vacation with Luigi, and Princess Peach to an island in the middle of the ocean. Unfortunately though, Bowser was ahead of the game, and kidnapped the Princess while Mario and Luigi were off having some fun. We are introduced to the most adorable character to ever join the Mario series, Yoshi!

Super Mario Bros. 3, NES:
 

Mario and Luigi take off across a variety of kingdoms in a search to save Princess Peach once again. We are introduced to the Koopalings, Bowser's minions, who have taken over each of the kingdoms Mario and his brother must get through.

Super Mario Land 2 (and the 6 Golden Coins), Gameboy:

When Mario makes his return from Sarasaland, we are introduced to Wario, who has stolen Mario's castle. Yes. Mario's castle. Princess Peach is very generous to our hero. Anyway, Mario has to travel to the six areas around his castle to retrieve 6 golden coins as to unlock his castle and take it back. Wario isn't actually evil, he only took Mario's castle out of greed.
 

Super Mario 64, N64:
 

The first game of it's kind, a 3D platform. This game shows the potential of the N64. This game has Mario chasing Bowser and collecting power stars within Princess Peach's castle by entering the paintings that are in it's many rooms.

Super Mario Sunshine, Gamecube:

Mario tries once again to take a well deserved vacation, only to be thrown into jail for mass vandalism he didn't do.  He is then sentenced to community service, cleaning up all of the graffiti with his trusty new Flash-Liquidizer-Ultra-Dousing-Device, or F.L.U.D.D. for short. We are introduced to one of the most annoying characters in the Mario series. Bowser Jr.

New Super Mario Bros., DS:

After 14 years of being out of the spotlight he had invented, platforming, Mario finds himself travelling across the Mushroom Kingdom once again to save Princess Peach. Although Nintendo didn't add a whole lot of new ideas to New Super Mario Bros., they did add a multiplayer mode where Mario could battle Luigi for star-coins. This would be the main-focus of future Mario platforming games. 

Super Mario Galaxy, Wii:

Bowser just had to leave earth, and take Peach with him. Mario is thrown on an unbelievable journey across the cosmos to collect power stars, and save Princess Peach. With a whole new array of power-ups at his disposal, it shouldn't be too too hard for our favourite plumber.

New Super Mario Bros. Wii:

Bowser decided to give Princess Peach a big cake for her birthday, with a big surprise inside. You know what that surprise was? Bowser Jr. and the Koopalings. Yup. I know what your thinking, Bowser is a JERK. I completely agree. Mario, Luigi, and two Toads decide to take the screen together to add a whole new aspect to the game. Now you can throw other players off the edge in competition, or aid your buddies and get them to the end, your choice!

Super Mario Galaxy 2, Wii:

Apparently Mario couldn't have, in all his glory, conquered every galaxy in the universe. Bowser also decided that he'd give space one more shot. Mario, along with his pal Yoshi, take off to rescue Princess Peach once again.

Super Mario 3D Land, 3DS:

After two adventures into space, Mario has had it. He's headed back to his roots to save the Princess this time.... with a little help from the Tanooki power-up! Yup, it's back!

New Super Mario Bros. 2, 3DS:

Ok, I have to admit, using the leaf for the Tanooki power-up was a little dumb on Nintendo's part, because we all  know that the leaf gives Mario Raccoon powers. But I'm not complaining, Nintendo has still made a couple of great games, especially because they brought the best Mario power-up yet! Did I forget to mention how much COINS were in this game???? I'm not kidding when i say millions. So have fun!

New Super Mario Bros. U, Wii U:

Mario and his team make their way through an unfamiliar part of the Mushroom Kingdom, to us at least, to get back to Princess Peach's castle, as Bowser has kidnapped her and keeping her hostage there.

Super Mario 3D World, Wii U:

In my mind, the best Mario game out there. This game has an interactive map, you can run around, and walk to that bush in the background. The only problem I had with this game, was the new power-up. I think Nintendo is getting a little desperate, but it was still fairly creative. All in all, still my favourite Mario game though.

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The Legend of Zelda​