It's a common courtesy, but not required unless you have a contract that says so.

Most workers in the US do not have contracts and can quit at any time, just as they can be let go from their jobs without reason.

Yes, two weeks is the norm. In Canada too.

In Spain (last I checked we're in Europe) the most usual are two weeks by default. Contracts can extend it or you can leave at once while in the "test period", fair because during this period the employer can fire you at once too without cause.

You can leave immediately even subjected to this clauses, but then you suffer a penalization (one day of pay each two days you cut). Most times, the company owes you money at any given time (holidays, extra pays), so it's wise to stay unless the new salary nulls the difference. Also it's always good to keep good will with former employers, you never know.

2 weeks is courtesy, and standard. In California, it's "at will" employment .. meaning, the employee can quit with or without notice, but the employee can also fire, with or without notice. That said, there's a lot of labor laws to comply with, so companies in practice don't just fire people at will (they can be sued by the now ex-employee). But yeah, in this part of the world, 2 weeks is courtesy. No courtesy is rude, and you're "burning the bridge".