Super mario is a classic my kids loved that game. I even enjoyed playing it but I think my favorite one is a dead lock between Donkey Kong Country and Mario Kart. Both of those were fun to play with the kids it gave us some quality time. You should be able to pick either one up cheap.
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Super Mario RPG was just so different and awesome for a Mario title. Absolutely loved it!!!
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Ahh Super Nintendo, the good ol'days.

Street Fighter II was my favorite game back then. I think it was the first video game to cause me real injury by playing it until my thumbs and fingers were calloused, blistered and bleeding, just another Band-Aid and I'm ready to try again. I loved playing Honda, Guile, Vega, Bison all of them really but my favorite character "my guy" was Guile.
http://www.youtube.com/watch?v=Q2vZ8xMUnxg&feature=related

The non fighting game fav was Super Mario World. We were such dorks. My brother and I would actually argue and fight with our friends and family about game time with this one.
http://www.youtube.com/watch?v=naD6mNeHIsE
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My favorites were:

The Legend of Zelda: A Link to the Past
http://www.retrojunk.com/img/art-images/zelda3.jpg

Super Mario All-Stars
http://www.retrojunk.com/img/art-images/super_mario_allstars__world_u_2003_06_29_110515.jpg
Source(s):
http://www.retrojunk.com/details_articles/1528/

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There were a lot of really good games for the Super Nes (its still the best console ever released if you ask me), but one really stands out especially if you dig RPG games. The last 2d Final Fantasy, Final Fantasy 3:

Its actually the 6th one released in the series, but only the 3rd one in the US (Final Fantasy 7 for the playstation fixes the numbering). I had very fond memories of this game when I was a kid. It had an amazing list of characters, a good storyline, addicting gameplay, some memorable scenes, a beautiful soundtrack, etc etc. It literally stomps over FF7 IMO if you don't mind the sprites

Since you like 2 player games, there's also Secret of Mana (RPG similar to Zelda, but with multiplayer) and the Pocky and Rocky series, solid games in my book.
Source(s):
15 years of solid gaming

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I never had a chance of owning a Super Nintendo console. However, I enjoyed playing SNES games by downloading an emulator which came with almost 300 ROMS. Those were very addicting, and still I love playing them time to time when I am bored of playing X-Men : Wolverine and Bionic Commando.

However, most of my favourite games from SNES were :

1. Super Mario World
http://www.overclockedgamer.com/wp-content/uploads/2009/07/SMW-OST-Front.jpg

2. The Legend of Zelda
http://www.gamersblogs.com/images/galleryimages/69/1163389131_mid.jpg

3. Donkey Kong Country 3: Dixie Kong's Double Trouble (Actually I love all 3 of these games)
http://www.donkeykongonline.com/wallpaper-800-600-dk64-n64.jpg

4. Super Mario RPG: Legend of the Seven Stars
http://gaygamer.net/images/SMRPG-Cover.jpg
Source(s):
http://www.emulator-zone.com/doc.php/snes/
http://www.rom-world.com/

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I have a number of favorites:

Super Mario World + Super Mario All-stars- was a pack-in with the SNES late in its cycle with SMW and the 4 titles from Super Mario All-Stars, so 5 games in 1!
Final Fantasy 2 and 3 (or 4 and 6 in Japan)
Secret of Mana
Pocky & Rocky
Street Fighter 2 Turbo
Zelda: Link to the Past
Donkey Kong Country 1 through 3
Super Bomberman 2- great multiplayer fun!
Super Castlevania IV
Super Mario RPG
Lufia 1 and 2
Zombies Ate my Neighbors
F-Zero
Illusion of Gaia
Super Metroid
TMNT 4: Turtles in Time
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You can't go wrong with Donkey Kong Country. If you liked Super Mario World, then you'll definitely like DK Country. It's sort of like the Donkey Kong version of Super Mario World. In Super Mario World, you ride Yoshi which is fun. But in DK Country, you get to ride an ostrich, a rhino, and a swordfish, which is extremely fun. DK Country also features some of the best graphics for the SNES, if you're picky about that kind of thing.

http://www.jpjuegos.com/wp-content/uploads/2007/07/windowslivewriterretrogameofthedaydonkeykongcountry-13e13crate-donkey-kong-country32.jpg

Also, I'd recommend Super Mario All-Stars. It features Super Mario Bros., Super Mario Bros. 2, Super Mario Bros., 3, and The Lost Levels. (Some very rare versions of the game also include Super Mario World.)
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Tecmo Bowl was a great football game. It was the first game I remember that had real NFL players. The good old days when I could actually figure out a video game.
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Street Fighter Turbo
Super Mario World

and, to add something different:

Metal Warriors

Which is really an outstandingly fun game, with great mechanics and a neat two player mode.
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Earthbound has to be my favorite SNES game, with Chrono Trigger and Legend of Zelda: A Link to the Past close behind.
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Mario Cart for the SNES has got to be my favorite. I have a lot of memories of staying up late on school nights with my older brother and battling. His contacts would fall out of his eyes because he would not blink while staring at the TV. I of course took advantage of his temporary blurred vision to beat him ;)
Source(s):
Life
http://www.gamespot.com/snes/action/supermariokart/index.html

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Only game that I truly loved for SNES that hasn't been mentioned yet is ''Super Castlevania IV''. This was one of the very first SNES games I ever had - I think I got this and ''Pilotwings'' around the same time that I got the console - and it really blew me away at the time. The games use of sound in particular just felt like a HUGE leap over the old NES system. Also, I recall those levels where the background would rotate around, to purposefully disorient you, feeling like a complete breakthrough when I first played through the game.

I loved the original NES Castlevania games, but I played the hell out of this one.

http://www.youtube.com/watch?v=8VMr602CmGc
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i like a variety of adventure games and action they are all good in different ways so i cant really choose a best as some are better than others in certain things
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Go super mario cart. I have the emulator on the computer and used to play that when i was 4. Good times, good times.
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Super Mario Brothers is the best i can't get enough of the game I have always loved the game.
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