I have been wondering this for sometime as I'm sure the answer is completely different for different people. So I shall list a few great 2D games, you may agree you may not.
RPG
Secret of Mana
Chrono Trigger
Shooter
Megaman
Castlevania (Not technically a shooter, but long range weapon)
Platformer
Mario Bros
Super Meat Boy
Original Game Mechanic
Fez
Braid
Fighter
TMNT: Turtles In Time
Street Fighter
Of course there are so many amazing games to list them all would just take forever. I happened to list a few of my personal favorites from genres. So what makes a great game? We have seen games recently such as Shovel Knight which well surpassed it's kickstarter goal in 2013 with Sega style graphics. It had little to no story involved in the videos/descriptions given. So is it just the gameplay mechanics that make a best seller? Ocarina of Time arguably one of the best games ever made, would it have been so great with crap gameplay mechanics. So I ask the forum what is most important to you in a game? Original gameplay mechanics, amazing graphics, amazing story telling, or a mix where one leads the other slightly? Obviously the perfect game would have all of these traits. Then you have other things to consider such as art design, re-playability, ease of use. So feel free to add your own most important feature.
For myself it is a mix of interesting original gameplay mechanic and story telling. The gameplay will get me invested originally, while the story makes me want to keep playing.
What do you think?