I see Core and Hardcore as different things. Most of the people here are talking of Hardcore how I would describe Core Gamers.
Core gamers are people who are quite heavily invested in video games, be it their library of games, accessories for games, knowledge of games and/or years spent on games. We tend to be able to appreciate a wide variety of games even if we tend to not particularly enjoy that genre.
Casual gamers are people new to gaming (regardless of size of library) or just play video games in passing. Some may become core gamers in the future, others become internet trolls, most just stay casuals. [from this point forward I will refer to Troll/casuals as "casuals" since the other two really do not apply. Just understand that when i say "casuals" I am not against casuals, being a casual gamer is fine.]
Hardcore is the demographic that designers and publishers are trying to target within the core gamer audience with the idea that a game will sell if you telling the core gamers, "Yeah, you might be core, but this is HARDCORE!" Most core gamers don't buy into the idea, but still see the game as fun.
However many casual gamers will see it as an easy ticket into being accepted as a core gamer. Because these casuals try to force their coreness onto the core gaming community by proclaiming how awesome their game is, we begin to look down on that particular game.
Take Halo for example. When Halo was first around, the multiplayer is best summed up as Goldeneye64's multiplayer on crack. Because Halo was so awesome at multiplayer the casuals joined in; no problem with that. The problem came when the casuals began to boast about their Haloness and how other games suck. You see, we weren't against Halo; core gamers love themselves some Halo. We were against the Halo boasting from the casuals. In time that hate against the Halo boasting became a hate towards Halo. The Casuals were missing the point: Halo is a good game and really fun, but it is one of many good games that are really fun.
Not all of this is the fault of developers even though they make games that target the "hardcore". a big part of the problem is the core gamers' desire to rank stuff. Look at "Best Final Fantasy" and "Best Legend of Zelda" For the longest time those were held by FF7 and Ocarina. Casuals heard this and saw another easy pass into the core gaming club and said, "All other Final Fantasy/Zelda games suck." Again, they were missing the point. Core gamers were looking story, characters, gameplay, innovation, music, flow. That's what we always look at. For the casuals, it felt like their thought process was, "FF7 is awesome... Why is FF7 awesome? Cloud is a badass. CLOUD DESERVES TO BE IN EVERYTHING!" For Ocarina, for many people it was just their first Zelda game, and if you're a fan of Zelda, you know you just fall in love with your first Zelda game; it is kinda irrational. there is nothing really to say other than, "IT IS OCARINA THEREFORE IT IS THE BEST"
Halo, FF7 and Ocarina had technically become the games that "hardcore" gamers play.
Then the backlash happens. core fans of FF7 and Ocarina had 3 options: pick a previous game to differentiate themselves from the casuals, pick a more recent game to differentiate themselves from the casuals (picking a game kinda helps determine their age, but not a perfect system. older (SNES) gamers tend to pick 6 (because it was 3), younger (PS1) gamers tend to pick 8. Again, not a perfect system), or remain dedicated fans and have a logical argument as to why they like the game in a word file ready to copy paste so other core gamers know that they aren't casuals. Same with Zelda: some went Link to the Past, other went Wind Waker, some stayed Ocarina/Majora.
In the cases where the casuals cannot grasp onto anything the core gamers like about a game (The game is too weird) or that they cannot beat the game (it is too hard); they just say the game sucks.
Casuals also tend to like Irate Gamer, but that is a different topic.
Well, I hoped you enjoyed my personal view on the matter. Please don't hit the quote button expecting me to respond, because I really don't feel like it. this is pretty much all I have to say on the subject.