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I see a lot of confusion here lately. Let me clear things up.
I know we all think of it as quitting in advance, but that's not the case, even if you tell them "I'm going to quit in 2 weeks." When you give your notice, whether it's 1 day, 2 weeks, or a month in advance, you're essentially saying "I quit, but if you need time to find a replacement, I'm willing to stay for x amount of time." This is just a courtesy. If they decline your offer or let you go early, it still counts as a resignation, not a termination. They can't fire you if you've already quit.
Quitting without notice can reflect poorly on you when using that job as a reference in the future, but it's only meant to benefit your employer. You should always expect the possibility that they'll let you go early, so if you absolutely need that last paycheck, you shouldn't give any notice. And if they do let you go early, you shouldn't expect to qualify for any unemployment or welfare benefits that exclude people who quit voluntarily.
The above may or may not apply to the poster below who "gave notice but didn't REALLY give notice," but it's possible she just threatened to quit and it was misinterpreted to mean she was giving two weeks notice. Save/print your e-mails in case you need to show proof to receive unemployment benefits.