I'm looking to dive into the best of what the system has to offer in the genre. Help me out. What, in your opinion, is worth my time? Feel free to elaborate, if you so desire.

Lufia 2
Chrono Trigger
Final Fantasy 4
Final Fantasy 6
Earthbound
Illusion of Gaia
Super Mario RPG
Breath of Fire
Breath of Fire 2

And if you want to veer into non-English (which I'm assuming you are based on the inclusion of the "Super Famicom" in the title), Seiken Densetsu 3. That game's so good you'll never be able to get into Secret of Mana again, and it'll fill you with many different flavors of rage that it was never officially localized. There's a fan translation out there that's really good, though.

EDIT: I suppose I should actually include some reasons for some of the less popular titles.

Super Mario RPG is the precursor to the Paper Mario series, and it was actually developed by Squaresoft back when that was a sign of quality, meshing their mastery of turn-based jRPG combat with the Mario universe in a way that's weirdly entertaining. It also has a great soundtrack, and you've probably already heard part of the soundtrack because of its prevalence in Youtube intros and such.

Breath of Fire 1 is a fairly generic, but enjoyable jRPG, while 2 introduced a twisted story and has a so-bad-it's-good translation that cares not for punctuation. Both are a lot of fun, and there are a few returning characters and cameos in the second game that make the first worth playing that much more. The second game also gives you a town as a home base of sorts (which was unique at the time), and there are a few different endings.

Lufia 2 is godly. The first Lufia has one of the worst random battle encounter rates I've ever seen in a game in addition to being an unremarkable jRPG that does little more than check the boxes of what a game in the genre is expected to do, but 2 does away with random battles altogether by having enemies show up on the overworld map so that you can avoid them. It also includes some of the most rewarding puzzles I've seen in all of gaming, and it alternates between having a sense of humor and gut-punching moments of drama without either being forced.

Earthbound is Earthbound. If you don't already know why you should buy this game full of hippies and bubblegum monkeys and play it repeatedly until your fingers hurt, then I'll pray for your soul.

Illusion of Gaia is the forerunner for Terranigma and one of the games made by Quartet, who had a tendency to include spiritualistic themes in their games just vague enough to get past Nintendo's religious censorship of the time. This makes it a weirdly deep experience at times, though there are a few places where you might have to look up a walkthrough thanks to some puzzles of questionable logic.

Everything I would recommend and more is in this solid list. Can't speak for the order the games appear on the list, it's all subjective anyway.
http://www.listal.com/list/rpg-world-snes-edition
If I had to pick just a few, then:
Chrono Trigger, for it's unique gameplay elements, multiple endings, and excellent visuals.
Earthbound, for it's unique setting and memorable story and music.
Secret of Mana, a fun action RPG
Final Fantasy VI, one of the best plots in an FF game

imo there's Chrono Trigger and FFVI, and everything else was kinda meh compared to the big 2.

Live-A-Live had interesting plots. Star Ocean 1 and Tales of Phantasia were technically ahead of its time. but they didn't really deliever the "whole package" like CT did.

"The Legend of Zelda: A Link to the Past"!

Final Fantasy V: It's far better than any other game in the series.

Dragon Quest 6 and Dragon Quest 3 (remake): Probably the best games in the series. (DQ5 has many issues, especially in the original version, that make it not that great, and the remake of 1 and 2 has (IMO) the worst music of any iteration of those games, plus DQ1 is shorter than the original (because they increased EXP gains drastically) and DQ2 is a bit too easy (except for Rhone Plateau, which is still dangerous).)

Also, you could check out the Romancing SaGa series; I haven't played the SFC installments (unless you count the PS2 version of RS1, but that version completely changed the game mechanics), but what I've played of the series I have enjoyed. The final boss of Romancing SaGa 2 has a reputation for being very difficult unless you exploit a certain spell that can prevent the boss from ever getting a turn.

Star Ocean is fantastic.

The entire Quintet Saga, from Actraiser, Soul Blazer, Illusion of Gaia to Terranigma.

Actraiser 2 isn't an RPG in the slightest, so that knocks that out.

Also, Secret of Mana is an amazing ARPG, it was supposed to be on the SNES CD!

I wouldn't really count LTTP as a RPG, but more of an action adventure.

There's also Star Ocean and Tales of Phantasia, but those are hybrid action RPGs...

Oh, Bahamut Lagoon is a Tactical RPG worth your time if unlike me, that's the sort of thing you like. (I can't do Tactical RPGs.)

The early Dragon Quest games along with V and VI were made for the SNES if you don't mind playing translations.

I know Final Fantasy Mystic Quest isn't a looker and is made to be easy, but it's quite an amusing game.

Final Fantasy V is actually my favorite one; it is a refreshing break from the drama of IV, and the angst of VI.

Some of the Ultima games were ported to the SNES if that's your thing too, but the perspective might give you vertigo.

Shin Megami Tensi. I have no clue how Nintendo allowed this on their child friendly console and I'm pretty sure these never made it to the west. There are several on the SFC.

Speaking of Secrets, there's Secret of Evermore and Mana 2 although the latter technically never made it over to the west.

Robotrek is an interesting one. You build robots to fight instead of putting your weak fleshy body in danger.

Lufia I & II is a pretty wonderful choice to go with!

That's about all that I can think of that haven't already been mentioned.

It entirely depends on your definition of "RPG"

Most definitely one of the best console games ever, of any genre.

Secret of Mana is probably my favorite RPG of all time. Mostly action RPG with pausing to cast spells. Good single player, great co-op. The way the weapon system works is fantastic, with each character leveling up their skills with each weapon independently. I really wish they would make a new Mana game in this style. Closest I've seen recently is Bastion.

Earthbound on the SNES is actually 'Mother 2', 'Mother 1', on the NES, which WAS going to be called 'Earthbound' was, apparently regionalised into English from Japanese but never officially released - there's ROM images of the unreleased English language Mother 1 / 'Earthbound 0' that you may care to find with a little googling...

Actually, I believe Mother 1 was released on the Wii U Virtual Console in the US. (Note that I have to say "in the US" because of region locking, which is one of the reasons I don't have a 3DS, Wii, or Wii U.) I believe the title was changed to something like "Earthbound Beginnings".


As I mentioned in a different topic, I don't consider Secret of Mana to be an RPG. It's still a good game, however.

The way weapon and magic skill leveling works is my favorite aspect of that game and I wish more games would take that approach. (Morrowind and Wizardry 8 both have somewhat similar mechanics, as does Final Fantasy 2, but none of those games are available for the SFC/SNES. (The SNES "Final Fantasy 2" is really just a modified version of FF4.) I think Romancing Saga 2 and 3 do something like this, and those are RPGs (though I dislike the "visible enemies that move in real time" approach those games use).)

If all you play is one SNES RPG, then please make it Chrono Trigger. This game is superior to any of the Final Fantasy games on the SNES (IV, V, and VI) and that's saying a lot coming from a major FF Fan.

It's got multiple endings, cool characters, catchy music, an engrossing time travel story, a simple yet deep battle system, and a New Game+ to play through it again with all your earned levels and equipment.

If you like the idea of Back to the Future as a JRPG, then this game is for you.

there was a cool Shadowrun game on SNES