Several people have recommended Fragile Dreams: Farewell Ruins of the Moon, I'll go more in-depth on why.
Fragile Dreams is a flawed masterpiece. There is no other game out there quite like it, and what it does right is does absolutely beautifully. It is a really beautiful game in several senses. But unfortunately for as much as it gets right, it also stumbles and makes big mistakes, and a lot of it comes from game design decisions.
Fragile Dreams at its heart is a game about loneliness and the need people have for interaction and others. You play as a boy named Seto, who we hear monologing at the very beginning of the game. The monologue comes from the end of the game, after his journey has finished. He recollects everything that's happened to bring him here, and as he reveals, at the end of everything, he is alone.
The game has a beautiful artistic style depicting an abandoned Japan left to rot away. It has a very strong artistic direction, and is one of the best-looking Wii games for its art style alone. It makes fantastic use of colors, symbolism, and the sort of beauty of a world in disrepair. This is backed by some beautiful music, the soundtrack to the game is just gorgeous. A few personal favorites:
Hikari
A Dedication to Everyone
Friends
Together with the Moon
Thank You
And there's a lot more. And it's backed by a pretty interesting story with some pretty likable characters. With that, the collectibles the game has are beautiful. Basically you find Mementos, and these Mementos tell voiced stories of varying lengths of people's final moments on the planet. Some of them are beautiful, some are a bit silly, some are a bit heart-breaking.
Game holds up because of all of this an amazing atmosphere, and honestly if this was all the game was, it'd be a beautiful game.
But the flaws come from the gameplay. The basic game is stylized like some sort of weird survival-horror meets action-RPG game, but it makes a lot of dumb design decisions. There's some absolutely frustrating parts, you have breakable weapons, there's some 'mini-game' segments and a couple of them are infuriatingly difficult and you need to complete them to progress, there's one section of the game where they make you back-track back and forth something like three times, and just some other annoyances like some enemies being able to stun-lock you, this one mechanic involving crouching and moving slowly and stopping over crumbling ground beneath you so it doesn't collapse.
But I would say the game is absolutely worth playing, especially as it can be found for pretty cheap, and it is a beautiful game that tells something that no other game has before or since. But I do agree with Jim Sterlings opinion on the game, even if I was more okay with the core gameplay than he was. I'm not quite as harsh on it, but it certainly is a case of a beautiful, original game that is let-down by some poor design decisions. What they get right is done beautifully, but what they do wrong is pretty ehh to bad.
Is Fragile Dreams worth playing? Absolutely, if you have the sheer willpower and patience to see it through. There is truly nothing quite like this game, on the Wii or anywhere else. However, the game makes so many unfair demands of the player and requires so much forgiveness that most won't want to stick with it. It's a horrible shame because the things that Fragile Dreams does right are done beautifully, and such a lovingly crafted world deserves so much better than to be forced into a poor game.
That's the biggest frustration with Fragile Dreams. That so much brilliance is let down by careless and slapdash game design. That a truly wonderful story is clouded by terrible combat, terrible quests and terrible wastes of time. That a title deserving nines, tens and nominations for game of the year has been relegated to the status of "alright" and "just about worth playing if you've got the stomach for it" thanks to things that not even the developers could have considered acceptable.
Fragile Dreams: Farewell Ruins of the Moon is beautiful. I thank the developers for making it. I resent the developers for not making it good enough.
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Also, while not something I'd really call obscure,
Silent Hill: Shattered Memories is a good game worth playing, the Wii version is by far the best version, and is one of the few games that got wii controls right. It also has a good story, atmosphere, and is what I consider my favorite 'walking simulator' type game, it does some very smart things that makes it unlike what you usually would describe as a walking simulator, but I think it fits in that sort of category.