What elements are needed to make a great 2D Platformer in your opinion?

Challenging and not repetitive.

platforms

3D.

Something different. You cant just release something from the 16-bit era and hope for the best, nowadays, all platformers need a hook.

Puzzles are a must in platformers nowadays IMO. #1 thing about a good platformer though is they all have great jumping mechanics.

Controls and level design

Dunno if that will work out well but you can use it as inspiration:

• A mechanic like in Prince of Persia: Sands of Time so you can rewind a few seconds? Needs to be well implemented to make the game hard enough, though
• A mechanic to slow down the time, to make otherwise impossibly fast passages possible
• Allowing the player to transform into another shape with the press of a key, for example a combat shape or a shape with better jumping abilities

Controls and animation. "Smoothness" and "feel". Fluid, without being loose. Solid without being rigid.
Level design. Navigation and any puzzling should be logical, natural, and with as few dead ends and non-secret nooks as possible.
Graphical style. Cohesive, and compelling.
Storyline. Present in the environments, characters, and events, but never gets in the way of gameplay.
Something new. If there's no intention to sell it, this isn't as important, but it's still good for making someone have a reason to start playing, amongst the sea of existing platformers.

Tight controls, challenging levels, good music, varied mobs.

The game must be challenging but with good difficulty not some cheap thing. A platformer has to have it's difficulty in the platform side of the game, most of the platformer i saw lately are half puzzle and I really don't like this, i mean i want to have difficulty to move from a part to another cause the environment and the enemies are trying to block me, not because some puzzle is slowing me following my path.
The level design is very important and also the movement in general should be precise and good.
I would look to 'super meat boy' to see how a good platformer has to be done, it's one of the best I last few years but even it has some defects for example this boss was a bit annoying, I don't know maybe it's me (cause the second time i've beaten it i made it fast) but it felt a bit cheap with those sequences of actions (always the same) with short time to anticipate them.

Kick ass fighting game with action missiles.

height and width(make sure not to accidentally apply depth)

Mario and Shigeru Miyamoto. :)

easy... be like Castlevania: SON
Example:
Dust: An Elysian Tail

The marker is currently saturated with indie platformers in the general sense, take that formula, levels + a gimmick or two + an artsy design and tip it on its head. Don't follow it. Don't be 'another indie platformer' try something different.

I've given her a link to this thread, she can't make an account because she doesn't have $100 worth of games, but she can follow it.

A little fat Italian plumber.

A steep learning curve, backtracking (metroid), exploration. The game must be hard enough, so that I can get frustrated with it. That way I'm driven to get better until I can master it (I wanna be the Boshy, Metroid, Megaman etc.)

Most games are just linear corridor jump games, but I love backtracking. Unlocking new skills and equipment and suddenly "new doors" open in areas I've been before until I realize at the end that the whole world (in a level sense) is connected from start to end and back.

I think the most important things are:

• Controls and physics - the character we are playing as must feel good to control. I should be easy to get and natural, jumping, running, stopping, all that stuff is important. It just must feel good to play, not like Cheetahmen or Captain Novolin.
• Level Design - doesn't matter if you are making a platformer or FPS - level design is one of the most important things in video games. It must be working nice with physics, always fresh and well thought-out. Without it player might just get bored, so you must keep him/her interested. Take a look at Castlevania SotN, Super Metroid or Megaman X. Secrets are very important to keep player playing the game. Easter Eggs can be nice too.
• Character(s) and abilities - you must think well about what platformer you would like to make. Should it be Mario style or Metroidvania style - you should give your character proper abilities. Depending on what game you are trying to make, it might be just a simple jump, like in Super Meat Boy. It might be bionic arm/grappling hook, like in Bionic Commando and Super Metroid. Some fighting ability. Different characters might have different abilities and physics (Castlevania 3, Super Meat Boy). Possibilities are endless, so think well!
• I forgot about one more thing. Good tutorial. It's the best if it's like in Megaman X or Super Meat Boy - it doesn't tell you what you must do, but you get that quickly anyway because of good level design. Tutorials like in Warioland 4 or Offspring Fling are good too - commands written on the walls. If the game has a story, you can put tutorial as conversation between characters - "Snake! To climb the ladder press the action button!". Almost the worst in my opinion are tutorial where everything stops and and a little box tells you how to play. It just feels unnatural and destroys the game's pacing. The worst is the gamepad button mapping while loading. Fuck people who invented that crap.

I just want to list you my favorite 2D platformers: World of Goo, Super Meat boy, Thomas Was Alone and Stealth Bastard Deluxe.

The best 2D game for me? Binding of Isaac. It has its climate, its own humour and is REALLY skillful and grindable. Plus it has great audio and visuals. I'd reccomend checking it.

HATS TO COLLECT/COLLECTABLE HATS

Carbon, oxygen, hydrogen and nitrogen,

Let her go a way like Terraria. No big campaign/story needed. People will be able to create their own stuff. :)