Afraid to do some research on what people wrote on your own? Wanna be bottle fed like a widdle itty bitty baby? Come on, take my hand...
7th Saga- One of Enix's RPGs. A common issue some folks had was how hard it could be when you got sent to the past, but if you don't have a problem with level grinding, that can be over come, allowing you to enjoy the rest of the game. Nice graphics, good music, and a decent story as well.
ActRaiser- Another Enix title, this one mixes a bit of Populous-like God playing in with the side-scrolling action sections. The graphics are quite nice for an early SNES title, and the music is very good. Offers up a nice challenge, without being cheap.
ActRaiser II- Want a game that'll make you cry? Here you go. Great graphics and some very nice music wrap themselves around the insane difficulty. The God sections are gone, making it pure side-scrolling, but being different from the first doesn't mean worse. Just be ready to swear at your TV screen a lot.
Axelay- A Konami shmup that uses extensive Mode 7 effects for half the stages, and regular side-scrolling stages for the other half. I find the 3D stages to be a bit dull in comparison, but the game still comes of well. Nice graphics, great tunes, and a solid challenge.
Biometal- A side-scrolling shmup from Athena, which Activision brought over to The States, and threw 2 Unlimited music into. The graphics are quite good, the music isn't bad, and this game will offer up a good challenge with an interesting sub-weapon.
Castlevania IV- Very easy, but quality entry in the franchise. Very nice music, great early SNES graphics, and a lot of stages to play through.
Castlevania: Dracula X- A pseudo-sequel to Akumajo Dracula X Chi no Rondo (Dracula X: Rondo of Blood), this game gets a lot of shit that it doesn't deserve. It has the same soundtrack as the CD-based "Rondo" (which the SNES does a great job reproducing), and uses a similar gameplay mechanic (rescue chicks), but it has so many different stages and such, that calling it a port doesn't really describe it. The graphics are great, the stages are good, and the only complaint that I feel can be leveled against it, are the "bounce me back and forth until I die" deaths that come from the painfully short invincibility time when you get hit.
Contra III: The Alien Wars- It's Contra. You know what to expect. Good early SNES graphics, some cool effects, and good music. Not as tough as other entries in the franchise, and the top view stages aren't as much fun as the side-scrolling ones, but it's still good stuff.
Cybernator + Metal Warriors- Part of the "Assult Suit" games (Target Earth on the Genesis was another), you hop into your Mech suit, and blast bad guys using various weapons. They look great, sound good, and the 2 player mode in MW is a blast. I love them, but they are a bit slower paced, and don't appeal to everyone. Try emulating them first to see if you're into it.
Demon's Crest- A part of the "Ghosts" and Gargoyle Quest games, it's a fine game that got overlooked by some. Fantastic graphics, very good music, and a solid challenge to get the best ending. Great atmosphere too, with some tough levels.
Firepower 2000- Top view shmup where you can play as either a jeep or a helicopter. Good graphics, good music, and a good challenge. Doesn't do anything revolutionary, but it offers up a fun "kill anything that moves" gaming session.
Gradius III- Yes, it has a lot of slowdown. And yes, it's missing the 3D stages from the arcade game. But those things aside, this is a good port of Konami's classic. There's not much else to say beyond... it's Gradius. Just get it.
Hagane- A Shinobi-esque platformer with some very good graphics, music, and a tough challenge. It didn't get a lot of attention, but if you enjoyed games like Revenge of Shinobi or Shinobi III, you'll feel right at home with this.
The King of Dragons- A straight-forward hack 'n slasher, where you choose from several character types, and slice your way through hordes of enemy creatures. Akin to Golden Axe and its ilk, it's simple, but fun. A solid port of the arcade game, with nice graphics, some good music, and a tough challenge.
MegaMan X- Do these need to be described?
MegaMan X2- I didn't think so.
MegaMan X3- Just get them. They're good.
Ninja Warriors- A sequel to Taito's Ninja Warriors (three screened arcade game), it's a good Final Fight-esque beat'em up with very nice graphics, good tunes, and a solid challenge. Choose from three different fighters, and go to town.
Nosferatu- What do you get if you mix Prince of Persia (DOS) with Dracula? Here you go. Very nice graphics, smooth animation, and some enjoyable music as you make your way through the castle and its ground to rescue your girl. It's a tough game, but it's fun.
Phalanx- Nothing ground breaking about this side-scrolling shmup, but it does it's job well by giving you plenty of stages, a good challenge, and so forth. It's just a solid shmup.
R-Type III: The Third Lightning- The SNES's best shmup in my opinion. Great graphics, great music, one hell of challenge, and a nice advancement in the classic R-Type gameplay by offering up three different force balls to choose from. If you like shmups, and you don't like this one, there's something very wrong with you.
Skyblazer- A forgotten gem on the SNES. Very nice graphics, good music, and a quality action title that's not too taxing on the reflexes. Plays a little bit like a mix of Actraiser with touches of Mario, with some flying stages to break up the regular platforming ones.
Space Megaforce- Top view shmup by the famous Compile group. It uses some cool Mode 7 effects in spots, but it's still basically a straight-forward blast-a-thon. Good early SNES graphics, some good music, and weapons that can be powered way the hell up. Lots of stages as well, and it offers different modes to play the game in.
Sparkster- Remember Rocket Knight Adventures? Here's the sequel. Plays much the same, looks much the same, but it's a whole knew group of baddies to get rid of. Great graphics, great music, fun gameplay, and a healthy challenge. It's different from the Genesis game of the same name, so even if you have that one, this one's a must get.
Star Fox- C'mon. It's Star Fox. Who doesn't know about this game? The FX chip does a nice job making the 3D world, the music is quite good, and having three different courses to play through (plus hidden stages) gives this game a healthy dose of replayability.
Sunset Riders- Straight up brawler in fine Konami fashion. Choose one of four characters, and go after the bad guy in Old West style. Good graphics, very good music, and it's a tough little game too.
Super Ghouls 'N Ghosts- Just get it. Hard as a fucking rock, but awesome in every way.
Super Mario All-Stars- Remakes of the three NES Mario games, plus the original second game that only came out in Japan. The graphics and music are redone to look like Super Mario World.
Super Mario World- Duh.
Super R-Type- This is, for all intents and purposes, R-Type II for the SNES with a few differences. It's riddled with slowdown, but the gameplay of the series still shines through. Very nice graphics, good tunes, and a solid challenge.
Super Metroid- If you don't get this, you should be banned. Arguably the best entry in the franchise. Great graphics, music, challenge, and a hidden ending if you can beat it fast enough.
Super Turrican + Super Turrican II- Like the orignal games on the Amiga, it's basically a run 'n gun with some platforming thrown in at times. Lots of action, a tough challenge, some fantastic music, and great graphics. The second game adds in CGI rendered graphics and some Mode 7 3D stages which can be pretty tough, but these games are quality action titles.
Teenage Mutant Ninja Turtles IV: Turtle in Time- It's not arcade perfect, but it's a fine game. Pick a turtle and beat the shit out of the Foot Clan. Very nice graphics, good tunes (though I prefer the Genesis version of those tunes), and while it is pretty easy, it's a fun game to sit down with for an hour and pummel away with.
UN Squadron- A shmup based off of the Anime, it's a pretty standard shmup by Capcom, but it's good. It doesn't break new ground, but it hits all its marks pretty well.
Yoshi's Island- Just get it. Don't ask why, just get it.
Zombies Ate My Neighbors- A top view action game that pays some heavy homages to horror flicks, it's just fun. Tough as nails, but fun. Great graphics, good music, lots of stages, and some good humor scattered about. You fight masked murderers and giant babies. What more do you want?
There. More info. And yes, I was just being a smart ass up top. Don't take it (too) seriously