I find Aquaria to be a wonderful case study in both game design and storytelling, and to say that it's good just because it's a "fun game" does a disservice the the sheer amount of love and work that went into this game. I've always felt that a good game is more than just a fun way to kill a few hours (or days, as the case may be). On the contrary, a good game should inspire us to think and inspire us to create. This is kind of the effect Aquaria has had on me, at least. I'm not ashamed in saying that this game more than any other helped shape how I see games and stories in general, as well as how I write.
To me, Aquaria's greatness comes down to two things more than all others: Music and Storytelling.
Music: Here's a thought experiment for you - shut down your speakers and play the game for a while. Just five minutes of gameplay should be enough to drive the point home. Take the music and sound away from the game and Aquaria is... Kind of mediocre, and much less touching. Music has a great impact on people. When music is matched up against the appropriate visuals and gameplay, it can take a fun experience and turn it into a truly magical one. The verse is central to the world of Aquaria in more ways than one might think. It not only made and animated the world in-fiction. It shapes our experiences as we explore it, it gives life to the visuals, it gives depth to the experiences and it gives weight to the memories we keep from them. Aquaria is - no pun intended - incredibly immersive, but it goes beyond that. It is also visceral. Some games try to make us care about their characters on an intellectual level, telling us why we should sympathise. Aquaria does not. It very rarely tells us anything. It makes us care on a much deeper level of feeling. Any game which can elicit an emotional response out of a player for nothing in particular is a true work of art. The music of Aquaria guides us, it puts us square in the emotion of the moment, and the story and settings work at a MASSIVE advantage because of that.
Story: I've said it before - Aquaria has very little actual narrative. The game has predominantly a single character who serves as protagonist and narrator, and the story consists of a literal handful of isolated plot points. However, that doesn't make it sparse or shallow. On the contrary, Aquaria's story is incredibly deep (again, no pun intended) and elaborate, as so much of it is told through the environment. At its core, Aquaria is not a story about events, it's a story about feelings. The plot follows not what happened, but rather what Naija felt on her journey. In her own words, we are experiencing her memories through her eyes. This isn't a story about a protagonist defeating an antagonist, or even a protagonist surviving in the wild. It is a story of a young woman coming to terms with who and she is, as well as with the world around her, at first finding it both fascinating and frightening, at first searching for purpose and meaning, but eventually settling in the comfort of familiarity, opting instead to define her own purpose instead of seeking to fulfil her creator's designs. And considering "the creators" is... Well, spoilers, anyway. Considering that, choosing to be her own being was probably the wise choice, all told.
But the story goes beyond just that. Naija is fascinating as a character, as well. She is constantly walking the line between truth and dream, as is the entire world of Aquaria. She is always somewhere between a sentient, contemplative creature asking questions and a feral beast just following her instincts and urges. Is her quest to find her creator one of sentence, or one of instinct, after all? As we see Naija exploring the world of Aquaria, what we are actually seeing is Naija exploring herself. With ever new experience she meets, she grows and evolves as a person. Having treasure collection as part of the game is an apt metaphor for the treasure collection of experiences. As Naija builds her home cave up from a hole in a rock, so we see her build up her personality from that of an apathetic sea creature just interested in survival into a real person. It's actually amazing how fluent this transformation is. When first we see Naija, she is confused, possessed by urges she doesn't understand, just following her instincts and exploring the massive new world that opens up to her, never making any real decisions or having any real goals. "Lost to the waves," as it were. But in time, we see Naija change into a person comfortable and familiar with her world, who shows initiative, chooses to face danger, chooses to make a stand and charts her own faith. For how light the story is on narrative, it's amazing how good it is.
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To me, music and story are what make Aquaria great above and beyond all else. And if you need an example of why that is, you need look no further than Capsized, an indie game that looks like Aquaria if you see the trailers, but which is completely different in feel and, in my opinion, at least, not nearly as good.