I get about 6 paid sick days per year (I say "about" because it depends on the number of hours worked). I use them when I need them, but that's rare, so I've accrued a fair amount of time. As far as I know, I cannot get paid for them if I don't use them, nor can I use my sick time to take care of a sick family member.
I work in schools--I don't get salary or benefits during summers--so I try to save up my vacation time every year to use during the summers. I confess that occasionally, when I need a day off--for example, to take care of my kid--I'll call in sick instead of taking the day as vacation time. But again, that's infrequent.
I don't like calling in sick unexpectedly, because it inconveniences my co-workers.