SPOILERS: THESE ARE UNUSED IMAGES IN SMB3 AND SMW. THEY ARE NEVER USED IN GAME.
There are actually unused sprites in SMB3, and Super Mario World.. * means that it is used in SMBX.
Golden Cheep Cheep and Green Para-Beetle:

Wheels and Spikes:

Beta Castle?

Unused Mario Sprites*

Unused Propellers:

Unused parts come up!
Koopas hosting the item mini-game:

Hammer Bros hosting mini-game:

Unused Mario Sprites (mini-game wise)

Early Ideas:
One powerup was to turn Mario into a Centaur (half man, half horse), though was rejected before development.
Objects:
The game's graphics reveal an item-sized Toad icon among some of the game's suits; it makes no changes to gameplay when granted to Mario. Later, this has been proven to actually be a Hammer Suit with palette errors, and it appears clearly in a "?" block in 7-8, giving Mario the Hammer Suit. There is also a powerup that acts like a Goomba's Shoe and also looks like a glitched one.
A set of blocks, with a large "?" block surrounded with smaller "?" blocks was also a scrapped object. This may have been something used in a bonus game/area.
Super Mario World
Super Mario World was going to be called Super Mario Bros. 4.
Red Coin (worth 5 for some reason)

Golden Mushroom (is a flying one and worth 1-up)

Some of the unused sprites in SMW (features early small mario and has Raccoon Mario)

Early level, possibly Yoshi's Island 1...

Early Map Images:

Unused Platform:

Purple Swoopers (they were intended to replace the boos, looks like Super Mario 64 Variant) and, also there is half of a purple spiny top... That's an unused sprite.

Unfinished Piranha Plant:

Small Door: (is actually half a regular door but who cares)

No Yoshi Sign:

Glitched Background:

Unused Translucent Mode (seen in early photos)

Dino Rhinos Breathing Fire:

Unused "Switch Palace 2" tileset header:

Unused sprites on overworld:
On the Map Screen, there were four sprites that were never used in the final game. All of them are accessible via certain hacking programs.
A Lakitu which circles around Mario's head on the overworld map.
A Blue Jay which flies around Mario's head like the Lakitu, but will follow him to the submaps, sans Vanilla Dome.
An animated Piranha Plant.
A Koopaling that doesn't look quite like any of the real Koopalings. It can force Mario to enter a level, like the Hand Traps of Super Mario Bros. 3. It ambushes Mario on the overworld. Because it was not finished, it corrupts Mario's position on the overworld map, and thus makes the game unplayable except for level 0, which is a never ending bonus game. Three copies of this sprite were actually used in the game. However, due to the specific setup of the overworld, players will never see them on an unmodified copy of Super Mario World.

Debug functions
Using the Super Mario World ROM and a hex editor, players may access debug functions that were left in the game. These include:
The ability to cycle through Mario's different forms using +Control Pad up + Select Button.
The ability to place Mario anywhere in a level using L + A Button. This can also be performed using a Game Genie code.
The ability to play in slow motion.
The ability to win a level with Start Button + Select Button.
The ability to have infinite star power.
The ability to change Yoshi's colors in the Overworld with Select Button.
Extra:
Yoshi was going to be playable on the NES, but it had to be saved up for the SNES due to the NES' limitations.

So yoshi was going to be a pterosaur... :/
SUPER MARIO 64
Yoshi egg:

Trampoline (top)

Trampoline (side)

Cactus (unused, possibly took 1 wedge away every time the player touched it)

Unused Flower in Lethal Lava Land:

Unused Key:

Unused Small Bully:

Cracked Ice:

Beta Shells (note that there is a red one)

Beta Bowser Fight:

Unused "U" texture:

Meaner Looking Thwomp (wouldn't it be better if they weren't blue?)

Early LLL (Lethal Lava Land)

Eartly DDD (dire dire docks)

Early screenshot of Super Mario 64:

Blargg (the texture is unfinished)

Early Penguin:

Early Pokey Sprite (MOVE FASTER, POKEY!)

Early Peach's Castle:

Early lethal lava land part 2:

Early Bomp:

Early Whomp's Fortress:

Mario with key counter:

Yoshi Egg in Motion:

Key Icon:

Unused Boo Key (say it fast and it sounds like "Spooky)
Early Ideas:
32 courses were initially planned for the game, but only 15 of them made it into the final product. In some sketch-ups of the game's early development in Super Mario History, Mario is seen jumping on a piano with the phrase ピアノの上よく(Well on the piano). He is also seen climbing a ladder, swinging around a pole, pushing a door and a block of ice, and crushing a rock with his head.
Luigi was also going to be playable but due to hardware limitations he was left out. But with Toad's Tool 64, type in L is real 2401 and it lets you play as Luigi. He has no gameplay changes. But, he was finally playable in Super Mario 64 DS, along with Yoshi and Wario. His stats are identical to Yoshi, except that Luigi has a bit of power.