In my position, I get 20 vacation days per year. In addition, the offices are closed the week between Christmas and New Years, so it's really five weeks per year. I can accrue up to 50 vacation days in my bank, then I lose anything over that.
For sick time, I get 22 sick days per year, and we can accrue 120 days before we start to lose it. I have been at the 120 day limit for sick time for a while (though I am on a sick day today, blah!). I've never been asked to provide doctors notes for the times I have been out on a longish illness (the flu, pneumonia, etc.) but I always get a note anyway, as they are entitled to ask for it.
My place is closed on all the federal holidays too, plus Patriots Day.