What criteria is most important to you in a video game?
Usually I look for new gameplay mechanics. I think that what made me like my favourite games of all time was this aspect. For example, the new 3D gameplay in Super Mario 64 and its various combat/utility mechanics, as well as Portal's unique teleport gameplay.
I also like it in games when there's a feel of achievement for reaching each area. I dislike it when the game is linear or entirely accessible right off the bat. It really gives a sense of progressive difficulty when in Mario 64, Rayman, GTA, Runescape or even Need for Speed you have to unlock one area after the other. It gives each area more important and makes them memorable.
I saw some of that in the Dragonborn DLC (having to take down those shrines one after the other before defeating Miraak) and was quite happy about it.
What about you guys?