That wasn't something I considered when writing this...  The visuals in a game also need to be something pleasing to the eye, or something now jarring to it. Wolfenstein 3D seems like a game that would be somewhat difficult to play as well as a bit confusing due to the graphics. Doom however is a similar to Wolfenstien, and I thought that game was impressive graphically.

I did think for awhile about games in which the graphics had a big impact on the gameplay, but I couldn't really think of any. Does the jump from 2D to 3D count..?

For me it really depends on the game. For a 2D plat-former, not as much - but I do love how great Max and the Curse of the Brotherhood looks and plays. But for a 3D realistic game I think they really matter.

Shadow of Mordor looks great! I am looking to see how Halo 5 or the next Elder Scroll looks.

It really depends on what I'm playing. On console, as long as graphics are fine and the game is good, I don't mind. That is, I buy a game regardless on how is looking. But on PC I admit that I become a graphics whore, even if it means losing some FPS. This doesn't mean that I don't like playing old games or indie with pixel graphics.
And it really depends on the game too. A game that has a gorgeous artistic style but doesn't push your machine to the limit is better than a title with great visuals but without soul (Bioshock vs Crysis).

As long as it's not overly blocky 3D then i don't care

In the middle. There are some things I'm really prickly about, for example I demand a decent AA in games, but overall PS4/XBO level of graphics is more than enough for me.

Excellent thread as usual Cloud. To answer the question, graphics are important but it's far from crucial in a game. There's much better things, like gameplay, music, story etc. after all, and whilst the graphical fidelity of the title can add to the immersion it's far from the be-all-end-all.

Graphics are the frosting on the cake for me; I value gameplay and writing before visuals in most cases and I'm prone to playing retro games quite often to get my fix since many modern games have shallow gameplay and writing but great visuals.

The best games are the ones that combine everything into an irresistible package; games like Half-Life 2 spring to mind. Other good examples are Bastion and The Banner Saga, on the small studio side of things.

You mean... like this??? >: )

They are important but they should come after good story and gameplay.

Yes..that and a few others. I can stand a lot of things but not that specific type. Like, how I'd have no trouble playing Genesis/SNES games again but PS1/N64 era games would be another matter, though it can vary by game.