Based on a manga of the same this anime is all about Tanaka Yukio, better known by his nickname Koyuki is a 14 year old who feels disconnected from life in general. Through the act of saving a mismatched dog BECK (the somewhat frankenstein looking dog or whatever you call it), he meets guitarist Minami Ryuusuke, and becomes involved in Ryuusuke's new band BECK. Koyuki's life starts to change as the band struggles towards fame.

Along the way he encounters many awkward and new situations, things he has never had to deal with before. If you've ever gone through things similar to what he's gone through, you'll immediately connect with this anime.(Actually I somehow dun like how the anime ends xp)
Beck relies heavily on this connection with it's viewers, so if you do not make the connection, you will probably not like the anime. It's not the standard slasher series, and focuses much on the viewers emotion.

So if you like music (Has an awesome rock soundtrack so good I even imported it) and storyline and want a break from the overplayed bloodshed scenario, this anime is for you. ^^