Video games have potential to turn into really good things. They're generally a lot of fun, but many provide thoroughly deep experiences that draw from traditions of literature, art, and film. I'm always on the lookout for a game that really aims to shift the paradigm towards increasingly sophisticated territory.
This list contains all the games I think are absolutely worth playing and why. They're all multisystem, and are at least on the PC unless noted otherwise.
Mass Effect - Futuristic RPG. This is a trilogy that develops narrative, philosophy, and characters like no other. The music's so-so unless it's incredible, the environments are usually blasé but sometimes extraordinary, and the combat is incredibly challenging in the latter two games (assuming you play the game like it's meant to be, on insanity difficulty, and depending on class. Once you're done, listen to this.
Bioshock - Dystopic survival game based on Objectivism. I liked both 1 & 2 for the emotional and intellectual depth, but the second doesn't really add much in terms of originality. If you think of it as an extension of the first game, and you don't really care too much about gameplay, you'll likely have as good of an experience as I did. DON'T look up spoilers.
Dead Space - Horror/Action. For a game where you're dismembering space zombies, you'll be surprised how close this game comes to art. If you're playing this game right, you'll either be terrified, disturbed, or really uncomfortable. It's a really engaging horror game that is carefully crafted and very fun. It's full of psychologically twisted macabre, and it's great.
Final Fantasy VII, X, and XIII - RPG that blends sci-fi and magic. The mythos these games create are each spectacular. They're all different and awesome. Cinematics top the chart. Each one is all around very compelling and are absolutely pieces of literature. VII and X are generally considered flawless. XIII has been greatly criticized, but it has qualities that exceed the other two by far. The gameplay in it is polarizing, and it is criticized for being very linear. But if you want a game that explores the religious relationship between humans and a hierarchy of deities on an epic and personal scale, or just see a handful of mortals destroy a god, then XIII is for you. PS1, PS2, and PS3 respectively.
Limbo - Short, grim puzzle game. It is very aesthetically-oriented and creates an excellent mood. Going through the game really builds it up, and by the time you've gotten to the end, the effects of the conclusion are tangible.
Pokémon Mystery Dungeon - If you enjoy Pokémon, and you enjoy top-view turn-based cave exploration, then the plots in these game are unexpectedly poignant. I was surprised when I actually felt a tear come to my eye in a Pokémon game, because they usually don't really take many risks with the artistic elements. Mystery Dungeon is, like, the only good spin-off ever. Game Boy Advance and Nintendo DS
Kingdom Hearts - A strange mix of light-hearted Disney worlds and the darker, very difficult story elements of Square Enix games. It's an action RPG with very fun gameplay. Doesn't quite break the mold in any particular way, but it's fun and trying to figure out the plot is rewardingly difficult. PlayStation 2 only, but spin-offs are on various systems. Chain of Memories and Birth by Sleep are the more noteworthy intermediaries.
Portal - 2 long, hysterical, exhilarating puzzle games. They require a unique kind of spatial thinking that will be stuck in your head for a while after finishing them up. Very polished, use many artistic elements very subtly and very well.
Heavy Rain - Interactive movie about the search for a serial killer. Very tense and creates a lot of drama. PS3 only
The Elder Scrolls Series - Western RPG; open world, medieval questing. They all stand alone, so get the latest one your system can handle.
Dear Esther - It's like a poem, it's really quaint and enjoyable to play through. It's subtler than any video game I've seen, mainly because it was developed by a professor who wanted to explore new artistic domain with the medium of the video game. There's really no gameplay, so you just explore an island and hear narrated letters as you go. When I finished, I was just staring at the screen until something eventually snapped me out of the daze.
The Legend of Zelda: Twilight Princess - This game is fucking amazing. Zelda games all share certain gameplay elements and notable features that make them stand out as fun, wholesome Nintendo games, but this one in particular has a gorgeous aesthetic and brilliant design. If you at all like the twilit aesthetic, then many moments in the game will really stick out for you. Wii & Gamecube (I suggest Wii)