Of all the 2D video games ever made, which do you think is the all time greatest, and what about it makes it worthy of the top spot?

Thats a bit vague. I mean its like asking what the best 3D game ever made is. It would just be your favorite game.

Super Mario Bros. saved the industry, I think this is not even a question.

If you're asking for my favorite, though, that would be Donkey Kong Country 3 due to how incredible it's exploration and secrets are. And all of that on a 16 bit system.

Greatest of all time?  I'd have to go with The Legend of Zelda on the NES just because of how much it did all at once when compared to everything else at the time - all the way down to the gold cartridge, full color booklet with story elements and the map that it came with.  I can understand people picking Super Mario Bros for the standards it set but I think Zelda's tight gameplay, level design of the overworld/dungeons and clever item usage will be timeless forever.  And you got an entire second quest included right there on the cartridge that felt way more expansive than what SMB and other titles' second play-throughs gave you.  

As far as "the best" 2D games of all time, you can add A Link to the Past (SNES), Super Mario World (SNES) and Castlevania: Symphony of the Night (PS) in there too.

Final Fantasy 6. I'm just kind of obsessed about this game. Gameplay is on the easy side, but playing with handicaps was a blast. Story, characters, vibes, music... loved it all.

Not far behind are FF4CC, Super Metroid, A Link to the Past, FF5, Symphony of the Night, Suikoden 2, Penguin Adventure, Maze of Galious, and Chrono Trigger.

There isn't a singular one. Too broad of strokes. Many different genres and goals and aims. Why I don't believe in a single greatest game either. Rarely a single best in a genre either to me. Rare exceptions like really niche and small ones.

Chrono Trigger is my favorite. I will not elaborate.