-Interesting or at least amusing characters. I can tolerate a mediocre story as long as I'm having a good time with the people going through it. (Tales games more or less exemplify this for me)
-Collectible systems that allow for gameplay progression or diversity (Pokemon, Persona) or add backstory/lore or at least cool character art (Metroid Prime, Batman:AA's riddles). Just make it more than GTA's nondescript hidden packages
-Exploration, as long as the game takes some form of creative license to make the world worth exploring. I love Morrowind of all the Elder Scrolls games in large part because the world seems truly alien, while I think that recent Rockstar games fail on some level because they choose to make a painstakingly accurate representation of the real world without considering that the real world is full of thoroughly uninteresting space.
-Soundtracks that consist of modern musical styles rather than more orchestral instrumentation. Rap, rock, country, J-pop, whatever works for me as long as they don't lean too heavily on metal. Licensed music can be great but doesn't really count
-A general lack of gritty realism. Gritty unrealism is fine, but I want my grit in moderation. The surreal, absurd, and fantastic are things that video games have a unique window into, and I feel that this potential is far from sufficiently explored
-Meaningful gameplay outside of just combat, whether it's puzzles, platforming, a strong conversation system, or just a strong sandbox element outside of just driving and shooting or something