Most places I've been have a distinction between personal or sick days (days taken with no notice) and vacation days which require at least 2 weeks notice before taking. Everywhere I've started I got 5 personal days and 10 vacation days.
In the UK, and I think most of Europe, sick days aren't limited and personal days would depend on company policy. Either can require documentation (doctor's note etc).
I have 30 days vacation, which is fairly typical. Giving twice the vacation length as notice (two weeks for one week off etc) is usually reasonable, but it's usually in the company policies.
Somewhere with unlimited vacation would need to ensure the employees used at least the legal minimum (20 days, plus public holidays).
