In my opinion, a hardcore gamer is one who plays hardcore games a lot, reads about games a lot, and loves games. And in order to clarify, I think hardcore games are games that are not casual games (or the new non-gamer games). I don't think a racing/sports/etc. game qualifies as a hardcore game because they appeal largely to casuals. Party games appeal to non-gamers and casual gamers too, perhaps some hardcore gamers but not much beyond that.
In my definition, a hardcore game is everything else, from Pokémon to Halo; from Mario to God of War. Every game made to appeal to hardcore gamers is a hardcore game. Therefore, my definitions of hardcore gamer and hardcore game go hand-by-hand.
I also don't think that a hardcore gamer has to finish every game to the max, to try to get the highest score or collect every item. I think those are collectors. A hardcore gamer, by my definition, is someone who plays games more than regularly, but a lot of time. I'm a high school student, and I like to be the best student, so that takes a lot of time from videogames. But in vacations, weekends, and on free time, I'll play videogames until I have headaches. Just to show, the game I've played the most in a single playthrough is Tales of The Abyss. I played 96 hours (!), not counting the Game Overs and after-defeating-final-boss-and-not-saving play time. I think, then, I'm a hardcore gamer (or was; that was somewhere in January-February). Today, I played some nice 7-8 hours, going back and forth my PS2 and my Nintendo DS. If that's not hardcore, then what is?
Ultimately,a hardcore gamer must love games. He needs not to have good tastes, but to know his likes/dislikes. He must learn to give unliked genres an opportunity (I, for instance, am willing to give MP3 and SSBB a chance, despite FPS (MP3 is FPA but I don't like the first-person perspective anyway) and fighting genres, along with sports genres, being my personal less-favorite) and to appreciate or hate every second he puts into a game, even if it's a bad or good game, ultimately a hardcore gamer enjoys just that. Being a hardcore gamer.
Then, by all of my definitions, I think most of us here are hardcore gamers. Those are my 2 cents.