1. Chrono Trigger
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One of the best games I've ever played, hands down. I don't really think there's anything bad I can say about this game. It even has great replay value.
2. Secret of Evermore
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Probably one of THE most under-rated games of all time, it gets very mixed reviews. I personally loved it. It has subtle humor and a great atmosphere. Every place you go is unique and the artwork and characters match these places very well. Prehistoria (the first place you go) is the only part of the game that isn't absolutely amazing, which is somewhat unfortunate since most people never go any farther. Antiqua, the next place after Prehistoria, is when the game really takes off. There are just little things throughout this game that make it very enjoyable, such as the "crazy" guy in Antiqua going on about how everyone is being controlled by a button-mashing overlord.
All-in-all, this game feels very smooth, it feels like an upgraded version of Secret of Mana (though the engine was built from the ground up, contrary to popular belief), with a much better atmosphere, character development, story, gameplay, everything. The Alchemy system was very enjoyable for me, as were the weapons system and the currency system. The only things I can really say bad about this game is that Prehistoria doesn't appeal to everyone and there are a few bugs throughout the game, some of which can be pretty nasty.
3. Final Fantasy 3/6
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A very popular game and for good reason. This game has a GREAT story and GREAT character development. Also, Kefka is probably one of the best villains of all time. This game feels like a pretty huge upgrade from FF2/4, with much prettier and smoother graphics and better gameplay/battle system. One thing that makes this game pretty unique from other RPGs, specifically the Final Fantasy games, is the fact that the main character is a female. Overall, this game is a winner, and I honestly can't remember anything bad about it.
4. Super Metroid
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Oh man, this game is just magnificent. Not an RPG, really, but it's right up there with my favorites. I've played this game for hours and hours at a time. I don't really know what it is about this game that makes it oh-so-great, but it is. The graphics are top notch for the SNES. The atmosphere is amazing, partially due to the graphics and partially due to the music. There's little-to-no character development, not a whole lot of story, but it does tie in to the previous game which is a bonus. Either way, you don't play this game for the character development and story. I would say this is arguably a near-flawless game.
5. Mario RPG: Legend of the Seven Stars
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A very fun and cute RPG. As far as the RPG elements go, it's pretty unique, and not really lacking in any way, but I don't think that is where this game shines. The story and character development/interaction is just phenomenal. There are so many memorable moments throughout the game. The graphics are pretty sweet and in general the game looks great. Not much bad to say about this game, really.
6. Breath of Fire
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This is, I think, a pretty underrated game. I don't hear many people talk about it, so I don't really think that people dislike it, but I think it slipped under the radar or something and many people just haven't even played it. It's a pretty old game and not really amazing as far as graphics or gameplay goes but the characters and story are great. In my opinion, a must-play, but not necessarily a must-play-again. I still revisit it, from time to time, but after the first play through it really doesn't beckon you back.
7. Illusion of Gaia
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More of a Zelda type game than a typical RPG, this game is pretty enjoyable. It's a pretty nice looking game, and the character development/story is great. It's a very mystical and majestic feeling game, having a lot to do with history and such. It can be a pretty difficult game at some points, but overall I can't say much bad about it.
8. Legend of Zelda, A Link to the Past
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Not much I need to say here, great game and gameplay, don't think I've heard many people say they don't like it. All-in-all, this game is a winner.
9. Final Fantasy 2/4
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I found this game to be pretty damn difficult at times, but the characters and story are pretty great. I still enjoy this game from time to time and there are some really memorable moments throughout the game. A real challenge, in my opinion, but really not as good as Final Fantasy 3/6.
10. Secret of Mana
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Probably one of THE most over-rated games of all time, it gets very mixed reviews. (See what I did there?) In my opinion, this game has many flaws, but I'm not going to point them all out. Instead, I'm going to point out the few good things about the game that make it worthy to be in my top 10. First of all, it's a cute game. Some of the music is great, while some of it makes me want to kill myself. The story has a lot of potential but really doesn't live up to it. However, the game itself is pretty fun to play. It has some memorable moments, even if the characters and story is lacking. The magic system is pretty nifty and I love how you can have more than one player. Really, I wish they had done that in Secret of Evermore. It makes for a lot more fun when playing with friends. Mainly, this game has "classic" value but other than that it's really lacking. I think this #10 spot could easily be filled by any of the Honorable Mentions, but I chose this one for reasons unknown. Even with its flaws, this game is loveable.
HONORABLE MENTIONS:
Super Street Fighter 2
Sim City
Earthbound
All of the Kirby games
Super Punch-Out
Final Fantasy Mystic Quest
EVO: Search for Eden
Terranigma
Super Mario World
Super Mario All-stars
The Mortal Kombat Games, though they lack in comparison to Street Fighter
Harvest Moon
Maybe Drakkhen