Steins;Gate
it's about a student who builds awesome but useless stuff in his room,
which he calls his 'laboratory', and accidently finds a way to send e-mails through time.
this, packed into an awesome story around friendship, love and death,
spiced with a bit science and time theory, makes one of the best animes i ever saw.
quote: "Just don't make the mistake to stop watching it after episode 3."
Mirai Nikki
The student Yukko has no friends and spends his days with writing a diary about himself.
In his fantasy, he creates the god 'Deus Ex Machina' who appears to be actually real,
and invites Yukko to a 'survival game'.
He and 11 other people get a 'future diary',
that can look several days or minutes into the owner's future.
The catch is, if they loose their diary, or if it's destroyed, they will die.
Only one can survive, because this one will be the next god of time.
Absolutely worth watching, but nothing for the squeamish.
Welcome to the NHK
The NEET (not in employment, education or training) Satou is a Hikkikomori:
After failing his graduation at university, he lives isolated in his room,
which he didn't leave for almost four years now.
On the first day leaving his house after more than three years he meets a strange girl,
that offers him her help to make him have a normal life again
and be able to live alongside other people.
Hikkikomoris - people that live isolated in their homes,
because they fear greater crowds of people and cannot live a normal live -
are a great social problem in japan and also other, even western countries.
This anime gives a good sight at the problems, never being too biased,
but rather funny. It's great and worth watching.
VC-MP: 
