Every year on our hire date anniversary, we get 40 hours of Sick Time. I think it goes up to 6 weeks-worth. I believe that, once the Sick Time is all used up, the employee goes on disability.
For "mild" illnesses, we are expected to use our Vacation Time, which accrues weekly, or our Personal Time.
Vacation Time accrues on a weekly basis, and how much you get depends on how long you've been an employee. Less than 1 year - .77 hours/week, 1-8 years - 1.85/week, and 9+ years - 2.77 hours/week. This coming June, I will start getting 2.77 hours per week. We are allowed to accrue up to 200 hours, and we are capped after that, but considering that 2.77 gives you 1 whole day off every month, that is still very generous.
Especially when you also factor in the Personal Time. We get 40 hours of Personal Time on July 1 every year. PT is "use it or lose it" - you don't carry over any unused PT hours past 365 days.
The reason Vacation time gets capped is because when you leave the company for any reason (even getting fired) you get paid for unused Vacation time. I'm up to 184 hours so, if I left tomorrow, I'd have almost 5 weeks-worth of pay coming to me. Personal and Sick, OTOH, we don't get paid for unused time when we leave.
Vacation and Personal Time can be used for any reason; in fact, we are expected to use up our Personal Time before we are allowed to start using our Long-Term Sick Time, which is no big deal anyway, since we'll be getting 40 more PT hours come next July 1.
As I see it, my employer is very, very fair and generous with their time off policies. We don't need to give reasons for getting time off, we only have to ask for it, provided that extended time off (like a week or 2 weeks) be given with far enough advance notice that the fill-in people know and thus will be prepared for the extra work.