I'm also in the US, and I receive 15 days of combined vacation and sick leave. So one bad flu can wipe out your ability to take an extended vacation.

Or, alternatively, you take only a day or two when the flu is at its worst, then come into the office to stare blankly at your screen and drool on your keyboard, whilst getting your colleagues sick. Yes, stupid policies tend to incentivize people to do stupid things.

You should have personal illness / sicktime in addition to vacation. If you don't ... that's sleazy.

Not in the U.S. At a contract packaging / manufacturing company I worked at, you received only one week (5 business days) of vacation after your first full year of employment.

I literally just walked out of an HR meeting where they brought in a lawyer to discuss questions like this and no vacation time is not required by US law (our company has roughly 4 weeks of vacation a year). In NY there is a minimum of 5 sicks days per year for employers with 5 or more employees, but again that isn't technically vacation time.