Hard Core
"Hard Core" (also written "hard-core," and "hardcore") is a generic term used to describe the most extreme, edgy, and intense portion of a given genre or fandom.
"Hard Core" music can refer to one of two different types of music: an offshoot of Punk Rock known for its rebelliousness, screaming, and emphasis on edginess over quality, and a techno off-shoot characterized by fast tempos and the use of atonality and dissonance.
In pornography, "hard core" porn features full nudity, sex, and various fetishes, while "soft core" porn tends to feature only partial nudity or the sort of (supposedly) tasteful nudes seen in magazines like Playboy. The official distinction between the two is, basically, "is there an erect penis on screen?"
In gaming, this is effectively impossible to define, but is usually thought of as those who believe that true "hard core" games require enthusiastic commitment and Casual Games should be ignored, if not locked out of "gaming proper" by definition (hmm...). In terms of marketing, there actually is a definition the industry uses for demographics to separate "core" games (i.e. games for gaming hobbyists) and "casual" games (i.e. games aimed at everyone). To put it another way, hard core gamers play for a challenge while casual gamers play for general fun, which is not to say hard core gamers are automatically "Stop Having Fun!" Guys. In fact, some hard core gamers will play at a disadvantage in order to create a bigger challenge.
When referring to fans, hard core can either be a perjorative ("Dude, did you see that guy with a Mario tattoo? I'm glad I'm not that hard core.") or complimentary ("That Mario tattoo is hard core, man.") Generally speaking, anyone who calls themselves "hard core" is either joking, a little too into it, or full of it.
In the Diablo series, "Hardcore" is the Self-Imposed Challenge Final Death mode for, well, hard core players.
Note that, in some circles, "Hardcore" can be used to refer to a work, rather than a fanbase. The usage varies depending on the medium involved; for example, a hardcore Anime is a sexually-explicit one, while a hardcore Professional Wrestling match or promotion is an extremely violent one with no rules and a large amount of Garbage Wrestling.