My company has unlimited sick days. I've used none in my 2.5 years here. It's not that I don't get sick, but somehow I get sick while on vacation. Yep that's fun.
I see the doctor for checkups, I had many appointments to accompany my wife to the OBGYN, and appointments for my new baby...I don't take time off for those.
If I'm feeling under the weather I stay home and do a bit of work. If I had actual sick days I would be more inclined to take an entire day off, especially if towards the end of the year.
When I worked for the govt I took mental days...day where it would be pointless to come to the office because I'm not motivated and would be unproductive. After a day off I'm good to go. Counted that as sick.