I noticed that there are some threads discussing movies but I couldn't find any with the specific topic of short movies.
Don't know if there's interest enough but thought to give it a try.
Let me know about interesting short movies.

Skhizein (2008)
It's a beautiful French short movie about a man who, having been struck by a meteorite, has to adapt to living precisely ninety-one centimeters from himself. I won't explain this further. ;)

But I will say this: AFTER you've seen this short movie, search for the meaning of the Greek word σχίζειν (schizein), so you'll get a better understanding of what the story is about. It's worth.

EDIT: The link for it (English subtitles):
http://vimeo.com/36824575

Rocket Brothers (2004)
4 minute long animation with music by the Danish band Kashmir. A humble story told with simple, hand-drawn artwork. Pixar, watch and learn!
https://www.youtube.com/watch?v=rkQsoyKoiWg

My local cinema still does short movie evening at least twice a month and also often shows a short movie before the main movie. I really like that as it's very interesting to see how the directors tell a story in just a few minutes.

Don't remember the exact names of most of the short movies I saw the last years, but I will write in this thread as soon as I see an interesting one the next time.

Ich hab noch Auferstehung (transl.: I still got resurrection)

Quote from IMDb:

"Marco and Lisa are in love. Online, they fight side by side against dreadful monsters. However, Lisa refuses to meet Marco in real life. When one day she stops showing up for the game, Marco decides to go searching for her. He finds a new world. And learns real dread. "

Trailer (with english ST):

http://www.youtube.com/watch?v=e4mC-_ufxC0

A wonderful movie. Just don't watch, if you love Hollywood endings.

MAMA Short Film:
https://www.youtube.com/watch?v=WRqS6pBC42w
This is the only short movie I can remember right now.

That is awesome! I wish more cinemas would do the same. Wow! I haven't thought about music video clips. I totally should. I just saw another one (Surfing The Warm Industry, link at the end.) from this band (Kashmir). And I found out there's a documentary called Rocket Brothers about this band.
Thanks for sharing this one. Real nice.
http://youtu.be/5-441uxB7Zw

In this case I would like to add Queens of the Stone Age - I Appear Missing:
https://www.youtube.com/watch?v=C9OfBcjyxKY
Also, another great short film:
https://www.youtube.com/watch?v=vVkDrIacHJM

Surfing the Warm Industry reminded me a lot of the movie Princess, about a priest who starts a bloody Vendetta against the porn industry. (EDIT: It appears that Morgenthaler directed both.)

Now for something else:

Modern Business Machines for Writing, Duplicating, and Recording (1947)
16:55 minutes of office technology so outdated it seems like science fiction. Sounds boring, but this movie sucked me right in.
https://archive.org/details/modern_business_machines_for_writing
(Play in browser, or download the large MPEG2 file)

Well, it took me a while, but I found most of the short films I have enjoyed over the past few years. Here they are:

The Witcher 3: Wild Hunt - Killing Monsters Cinematic:
https://www.youtube.com/watch?v=c0i88t0Kacs&list=UUzybXLxv08IApdjdN0mJhEg

Game live action films:

Sleeping Dogs

Deus Ex: Human Revolution

Skyrim

Someone made this awesome short:
https://www.youtube.com/watch?v=L0DsvpE9aOk

A short film for the book 1Q84 by Haruki Murakami:
https://www.youtube.com/watch?v=eF-SQGyPyDc

Short animated movie:
Sub Wars

Source Filmmaker:
This guy makes awesome shorts:
Zachariah Scott
There are some many others I would like to mention here. But the list would go over 100. I'm not kidding.

I hope you all enjoy some of these.

Sight, a sci-fi short film way beyond the Google Glass technology.
http://youtu.be/lK_cdkpazjI

And on the gaming related side...
Assassin's Creed for Kinect Announced! I think it was an April Fools Day movie.
http://youtu.be/7NufHsmITjM

Goofy Goat Antics (1933)
This is one of those flicks where the animation is timed to fit to the music track. It is directed by Ted Eshbaugh from "Official Films". The movie is a fragmented flow of visual gags, dancing and violence, with just enough continuity to make the constant changes of focus unsettling. The movies distaste of story and consistency is clearly demonstrated when what we through was a main characters walks into the glee club. The movie cuts to the inside the house, but she's not there. She has simply disappeared from the movie.

In a sequence which really reminded me of a Jim Woodring comic, the film completely abandons the rules of the physical world by creating what IMDb.com describes as a "Anthropomorphic Musical Instrument". Before that, two pig-playing musicians were melted for no logical reason.

Actually, this cartoon is a bit trippy. I have ended up loving it, after repeated viewing!

https://www.youtube.com/watch?v=OcOtkXwu8k4

The riddle from the scifi flick John Dies at the End:

https://www.youtube.com/watch?v=9rQC7XC79w4]

R.I.P.
http://vimeo.com/47179236

Nice, Sight is awesome, well made.The CGBros make some very interesting shorts. This thread is a great idea, thank you capile2, I love it.

Well, I thank all of you for participating in this.
You're posting so many nice things.