Originally the Japanese term for "house (more specifically, your house" in the honorific form of the language, made by adding the prefix "o-" to the word for house "taku." It can also be used as an honorific second-person pronoun.
Today, the word has taken on a different meaning: it refers to a person who has had or is in the middle of having an intense hobby, which is usually added before the word itself. See the example below (1).
The connotation of the term varies in relation to the speaker and how much said speaker knows about the actual context in which it should be used. Especially common among American fans, an otaku is simply a very devoted follower (2). However, the word has a harsher, more negative connotation in Japanese. It is a term that refers to the receiver of the description is a very reclusive, sociopathic person who has a severe addiction to any form of media and (in some cases) will rarely, if ever, leave his or her house to meet minimal living requirements or obtain more of said media (hence the term otaku derived from its original meaning refering to a house)(3). It is not to be confused with the term "hikikomori," or a person/people who has/have withdrawn from society. It is a dire insult, especially to those who do not actually fit the category of otaku.
Otaku (plural) are generally looked down upon in Japanese society, constantly derided for their passions. These insults may or may not have a penny's worth of truth, but they base themselves in preconceived notions of how previous people of obsession have acted. The otaku do receive a lot of scorn from their fellow peers, and hate crimes against them are not all that uncommon (4). Nevertheless, the word is not completely negative. For example, the largest anime/manga/East Asian convention in the United States is named "Otakon", and there is also the American-based "A-kon" (5). Several people worldwide have made attempts to remove its negative connotation, but have not been completely successful.
anime otaku, manga otaku
(2) American Usage, two boys
"I haven't left my room for days, I'm totally addicted to One Piece."
"Dude, you're a total otaku."
(3) Japanese Usage, one girl approaching a boy; the girl is stopped by a group of her peers who reprimand her advance
"Hey, you might want to stay away from that guy. He's an otaku."
(This comment is usually followed by sounds and/or remarks made by the new girl and/or the group itself.)
"Like the hikikomori type?"
"Nah, he actually leaves his house to buy groceries."
(4) Mention of hate crimes against said person/people
"In 1989, a man named Tsutomu Miyazaki became known as 'The Otaku Murderer' for his crimes which specifically targeted otaku."
(5) Two people mentioning Otakon
"Hey, are you goin' to Otakon this weekend
"Hell yeah, I'mma be outa money by Sunday! You?"
"Wish. I gotta lot of make-up work for 'being sick' during that last convention."