This unusual little piece of interactive art, The Graveyard, showed up on Steam recently. I wouldn't pay the 5 bucks for the full version, but playing the demo gets you pretty much the whole experience. It's quite haunting and poignant.
Another interesting, unconventional interactive "game" is Gravity Bone. It's weird to say the least.
For the most part, these types of games are a little too pretentious, but these two caught my attention.

I consider most of these experiments, which could potentially lead to something new so I am for it. You never know what will come of unconventional ideas.

Mmm.... 4€ for "visiting a graveyard as an old lady". No thanks.

Try the free demo. Basically all you pay for is the "extra feature" which is death.

I'm glad these type of things are beginning to show up in interactive media, it means that someone is finally getting that our favourite medium can be used for something other that shooting demons in the face.
Regarding that particular game (if you can even call it a "game") I think it's very interesting and daring as a concept.....and it quite strikes home since i found it also very, VERY sad :)
Of course this is by no means a "game": it's just an experiment with the medium to try something new (like PieceMaker42 said).
But try to think at a sequence exactly like that as a game ending: the protagonist is old (after the events narrated in the game), slowly walking a cemetery with his cane and looking for the tomb of a loved one long lost, and when he finds it, he dies.
That would be the best (and saddest) game ending i could think of, and would be extremely effective.

The ending in Hitman: Blood Money was set at Agent 47's funeral. The sequence was still just a shoot 'em up scenario, but it had a similar effect. The first time I played that ending in Blood Money, I didn't even know that he could wake up. But then after taking care of the agents, you still had to go and eliminate all the witnesses. Very fitting for the 47's character.

Best Ending Ever.

I would pay for a game like Gravity Bone, seriously. It was fun.

I've tried the demo and is really boring. =(

What'd you expect from a title like "The Graveyard"? It's not meant to be exciting. It gives you the chance to experience a small moment in the old woman's life. Not much happens, but it's more meaningful if you use your imagination and read into the circumstances of the situation.
Another pretentious game that tries way too hard to be artistic and philosophical is the one that I just finished playing yesterday, Metal Gear Solid 4.
<SPOILERS>
Imagine in the graveyard sequence at the end, if Snake had just done something similar to the above old lady scene instead of having a long winded conversation explaining shit that I didn't really care to know. On the other hand, right before that ending when Snake was crawling through the tunnel blasting with microwaves as he gets progressively weaker forcing you to jam on the triangle button with increasing frequency, was quite powerful and engaging. It really allows you to feel Old Snake's struggle to push through with all his will.
</SPOILERS>
That's the problem with Kojima though, he has a message to deliver in his storytelling but he just does so in such a convoluted way. Sometimes I'll be listening to some dialogue in MGS4 that makes me realize how insightful Kojima can be sometimes. And then he goes and makes characters spout some long drawn out inane explanations.

I wanted to try this for a long time, after I saw The Endless Forest. Downloading the demo as I speak... I really like all these original story telling. The last one which caught my attention was from Distractionware, Pathways.
-- Well... I've got to say it didn't amazed me as much as I hoped.

Fungoo, that graveyard scene was actually the one part of MGS4 where I thought Kojima got it right with the direction.
I get what you're saying about it, because yes - it was more needless wordy Kojima exposition, but it was also the one scene that wasn't completely overplayed. There was no added melodrama, it just happened and the camera was there to see it. I wish the entire game had taken that sober approach to directing.
It actually reminds me, I wanted to make a thread about naturalism in videogames. Perhaps now I will.

I just suddenly remembered another game whose title is escaping me at the moment. The premise is that you're visiting your old friend and his wife who are throwing a get together with you. The whole thing takes place in the apartment where you go in and type whatever you want to say and they'd respond accordingly. The limitations are inevitable, but it's surprisingly versatile in recognizing your comments.
Of course the first thing I said was to the lady, "Nice tits." She acted all embarrassed and pretended like she didn't enjoy it. But I knew better.
Someone might remember the title though. It was fully 3D but had this flat shaded rendering style.

Facade.

Couldn't you define most artsy fartsy games as indie games?