Earlier quoted context omitted.
Where are you located where two weeks' notice is law? If you are in an "at will" state, the law applies in both directions. Two weeks is a professional courtesy . An employer that is neither deserves nothing.
I've seen contracts that say both "at will" and "14 days notice required". Not sure if those are in conflict. It doesn't really matter, though. Always give 2 weeks notice, as professional courtesy, but also take any of your fragile or expensive stuff home first. Depending on your employer, you may not even get a chance to revisit your desk, and instead may be escorted to the door and met with a box of your belongings…
The "at will" we are talking about here are typically employees in US states that were not offered an employment contract.
You are free to go when you please, just as the employer is free to fire you at any time (not counting certain protected classes and etc)