Anime

What is anime?

In Japanese terms, anime (アニメ) pretty much means any kind of animation in general, but among the westerns it has been widely used as a synonym specifically for the Japanese animation. Even though it hasn't been long since it's introduction to the western world along with manga, anime has gained pretty considerable popularity mostly due to it's exotic drawing style. Some of the most popular titles known to the westerns are Pokémon, Dragon Ball and Naruto

Some of the famous ones

Pretty brief list of some of the most famous anime series on Nico Nico Douga, followed by some of the songs from these series:

• The Melancholy of Haruhi Suzumiya: The "everybody's favorite anime", this series is famous for it's huge fanbase and dance used for the 1st season's credits song, Hare Hare Yukai. This anime is about the daily life of the SOS Brigade, created by school girl Haruhi Suzumiya for searching time travelers, aliens and espers and to "have fun with them". Story is pretty much told from the perspective of Kyon, the main male character of the series, who makes contact with the ones Haruhi is searching for as the time passes by
  Hare Hare Yukai - Ending song from the 1st season
  Koi no Mikuru Densetsu - Opening song from the 1st episode
  God knows... - Insert song from the 12th episode
  Yuki, Muon, Madobe Nite. - Character song for Yuki Nagato
  Maggare ↓ Spectacle - Character song for Itsuki Koizumi
• Lucky Star: Based on the popular manga by the same name, it has gained major popularity in Nico Nico Douga by MADs and character songs. Series follows a pack of girls as they are living their high school lives
  Motteke! Sailor Fuku - Opening song
  Ne-Ni-Ge de Reset! - Character song for Tsukasa Hiiragi
• Higurashi no Naku Koro ni: Started as an one-man doujin game, this mystery game has been followed by numerous sequels, manga and anime series. The series follows a mysterious summer night of 1983, when suddenly people starts to end up dead with no apparent reason. And after everyone has gone, the night seems to repeat itself, and only one remembers what had happened...
  You - Ending song from Higurashi no Naku Koro ni (Meakashi-hen) game
  Higurashi no Naku Koro ni - Opening song from the 1st season
  Naraku no Hana - Opening song from the 2nd season
  Taishou a - Ending song from the 2nd season