Differs from company to company. In my case, there is a sort of pool of days that can be used for sick days, vacation, holidays, and so on. I didn't take paid sick days (that is, I was off but without pay) back then 'cause I wanted to save this stuff for if I needed it, and then found out that, well, it counted against me to take off for being sick and I could lose those paid off days. So as far as I'm concerned, I don't really have sick days. Mind you, I'm probably wildly misinterpreting my company's policy as I'm not used to having paid days off of any kind.

Some companies (and some government agencies) let you roll over unused days into a following year or get some kind of bonus or whatever for not using sick days. Mine doesn't, and doesn't roll over unused vacation time either.

Somebody who knows more about this stuff should correct me, of course.