Anti-Climax Boss: Your final fight with Bowser. The ability to touch Bowser's lower part of the body and not take damage can be exploited (if you're in Super form, just crouch). Add to the fact that the floor crumbles every time Bowser stomps on you, and you just have to wait until when you have to dodge on the very moment Bowser slams through the final layer of the floor and falls to his doom. This is Boss Arena Idiocy at its best. Averted in the GBA remake, as the strategy was an unintentional glitch that got fixed, so you'll have to dodge if you don't want to take any damage.
World 5-3. Kuribo's Shoe. An entire generation of gamers can bond over how awesome that level was.
Although not quite as awesome as 5-3, 4-6 contains doors that change the size of the enemies between the giant size typical of world 4 and the standard sizes found elsewhere — kind of a 2D precursor to Tiny Huge Island from Super Mario 64.
The treasure ship, which shows up if your score and coins meet a certain criterion. When you go to it, it's kind of like a Doom Ship, except covered in hundreds of coins. It is glorious.
Level 6-8, aside from the fortress levels, has absolutely no ice gimmicks at all and it is the only level whose design looks like it belongs in World 1 being made up of grass. The level itself is straightforward and contain a lot of chuckable blocks.
Some consider the final tank level to be a breather level compared to the rest of World 8. Sure, it has lots of bombs and cannons, but compared to everything before, it should be cakewalk at this point.
Broken Base: The reveal that the game is actually a stage play, along with the various theories pointing towards such before it was officially confirmed, have been met with all sorts of "ruined childhood" comments with lots of debate within the fandom on which versions of the game it applies to and whether it matters in the first place.
Demonic Spiders: Boss Bass, who can be found hanging around most of the stages in World 3, and has an annoying habit of swallowing Mario whole irrespective of what power-up you're using, instantly costing you a life. The Fire Chomps (especially in 5-9) can be this too.
The Koopalings went on to become an entire Darkhorse Ensemble.
Kuribo's Shoe. Despite appearing in only one stage, of one world, of one game, it is enormously popular, so much so that some fan-made hacks, such as Mario Adventure, made sure to let it carry over to every level. Years later, it makes its return in Super Mario Maker.
The Hammer Suit. Doesn't appear much (and hardly at all outside this game), gives you the power of an Elite Mook, and the hammers defeat quite a few enemies that fireballs can't. It also makes Mario immune to enemy fireballs if he ducks while wearing it.
Even Better Sequel: As important as the first game was, many regard this as the game which really set the bar for how platforming games should be done, and still consider it one of the best games ever made. The secret behind this success is that the game manages to preserve the original formula while introducing several new elements to keep it fresh, so it's neither a Mission-Pack Sequel like Lost Levels nor a Dolled-Up Installment of another game like Super Mario Bros. 2.
The Angry Sun can be this to younger players. The fact that it flies after you doesn't help much. Especially so in 8-2 where it suddenly comes at you from behind a hill in the dark.
Boss Bass can be just as frightening. A fast moving fish that can eat Mario in one bite and God help you if you fall in the water without the Fire Flower power-up. It makes you wish you had the Cloud power-up to skip the stages altogether.
Bowser's letter to Mario was the stuff of nightmares.
One-Scene Wonder: The best power-up ever, Kuribo's Shoe. It only appears in one level, and has yet to appear in any subsequent games in the series; the closest it has gotten to reappearing has been in a Continuity Nod in Mario And Luigi Bowsers Inside Story, a somewhat similar "Goomba's Shoe" item in Paper Mario: Sticker Star ("Kuribo" is Japanese for ""Goomba"), and an ice skate power-up in Super Mario 3D World that you can get by knocking out the Goomba in the skate. It finally re-appears for a proper worldwide release in Super Mario Maker, along with a giant form of it, no less. A subversion comes from its GBA remake, Super Mario Advance 4, where an exclusive e-reader level uses the shoe (this time inside of an ? block) as a major focus. However the level was only released in Japan.
Polished Port: The GBA port of this game, Super Mario Advance 4, boasts the upgraded graphics from Super Mario All-Stars as well as adding new levels via e-Reader cards. Though the e-Reader's failure prevented many people from accessing the new levels, the Wii U Virtual Console version of SMA4 makes them all available without the need for an e-Reader.
Seinfeld Is Unfunny: So many conventions for the Mario series were established here that younger gamers will be scratching their heads wondering what is the big deal with this game.
That One Boss: Ludwig von Koopa may be an even harder boss than Bowser. Every time he jumps he causes the room to shake for several seconds, immobilizing the player character. Worse still, the room is laid out in such a way that he'll often take a series of short hops from one side to the other, meaning there's no way whatsoever of avoiding him if you get caught in one of the tremors.
The airship in World 8. It is not like the Koopalings' airships. This one scrolls faster, and consists mostly of small platforms with lots of space between them.
The latter third of World 7 will usually be enough to drive all but the most dedicated players to use their Warp Whistle to go to World 8.
World 7-4. Not only is it an underwater level, the screen scrolls automatically, and there is a minefield of Jelectros you have to maneuver through.
World 7-7. A level plain filled entirely with Munchers as far as the eye can see, making the only ways to pass either using a P-Wing, which is Too Awesome to Use, or the intended mechanic, which is collecting every Super Star along the way to remain invincible throughout. The only problem is that the ? Blocks are spaced far enough apart that Mario must run at full speed or he won't reach the next one before invincibility wears off, which in turn makes the blocks very easy to overshoot. If that happens, you are dead.
Several levels in worlds 6 and 7 of Super Mario Bros. 3 require ducking through a one-block-high hole to pass, something that can't be done if you're in the Frog suit. And in at least one of them, you can't even commit suicide by way of Bottomless Pit. Considering how difficult it is to maneuver on land with the Frog suit, why would you use it prior to entering a level with no water? If there are no enemies nearby to run in to, you have to wait for the timer to run out.
It's impossible to do without cheats, but using the Kuribo's Shoe in a water level will cause the player to sink to the bottom instantly, rendering some levels completely impassible. If you're using an emulator which can disable cheat codes it's not so bad, but if you're using an actual NES with a Game Genie, you're screwed unless you can somehow bypass the water stages.
In the original NES version, a highly specific one involved grabbing a Hammer Bros. suit in the middle of a level (which happens once in the entire game; the others are Mushroom House prizes) while wearing a Tanooki Suit and activating the statue form. This meant it was impossible to go through pipes, and as said suit was in an area accessible only via pipe, it was one loss of a life for anyone who tried. Corrected in rereleases.
Woolseyism: The Koopalings weren't actually named in the Japanese version of the game. Their individual names were added in by the English localization, which explains why the DIC cartoon adaptation gave the Koopalings vastly different names.