My relationship with video games has become somewhat tenuous. It seems that all the things that have become popular don't appeal to me. I guess growing up during the resurgence of the video game industry in the mid-80s kind of defined the frame of reference I have for gaming, which affects how I react to the latest generation of video games.
Graphics do NOT impress me. I grew up with 8/16 bit games. Games that are STILL legendary today, and their fame has NOTHING to do with their graphics.
Difficulty is important. Most games today tend to be obvious/dumbed-down. There's no difficulty in gameplay, so the challenge becomes getting a bunch of awards or achievements. I don't care if I unlock the "X" costume for "Y" character. I care about finishing the game. If I can beat the game with little or no effort, then it's just a waste of time. I remember playing Gradius III for the SNES, which ironically was an easier version of the arcade game since Konami WANTED you to finish the game at home, and having my sister walk in during one of the levels and she gasped in surprise to see me fly my spaceship through what looked like an impenetrable wall of bullets and lasers. It took me days of trial and error to find the exact path to take, but once I figured out how to do it, I felt like I had earned something! After a series of levels like that, when I finally beat the game, THAT was the accomplishment that made it worth playing the game.
Story is MOST important. Every game I enjoy has a story that appeals to me. From Super Mario Bros. to Prince of Persia:Sands of Time, from Gradius to Metroid:Prime. If I don't care about WHY the character is going through the events of the game, I won't care to play. From the simple, primal story of Super Mario Bros., to the more complex story of the PoP:Sands Of Time, you care WHY these people are doing what they're doing.
The latest generation of games seem to be focussed on bigger and better graphics and not on anything else. It's deeply discouraging. To be completely honest, I constantly ask myself why I don't just drop video gaming entirely.
The answer is that every once in awhile, there comes a game or a game series that redeems the industry. The last one in recent memory for me is the Prince of Persia Series on the PS2.