I get unlimited sick leave (though obviously if abused HR will step in, and there are some rules, but I can take a day/afternoon off if I feel bad basically whenever). The only catch to the unlimited sick leave is a prolonged single leave requires certain information from your doctor and may be turned into a "leave of absence" which has a different pay scale.
On top of that, I get 10 days vacation + 1 personal holiday. The personal holiday is just a vacation day that has hours which must be used in the calendar year and don't rollover, normal vacation can be stacked up to 240 hrs before you have to use it. After you have been with the company a while your alloted days per year goes up, limiting at 20 days a year after 20 years.
I work for a Division of Emerson Electric Company btw, and seeing as there are 142K employees under that umbrella, I assume that other Emerson companies have different policies. Also we have 2 classes of employees, Exempt and Non-Exempt (Hourly). Hourly people have limited sick leave, but can earn overtime, Exempt have unlimited sick leave, but earn no overtime. Though I don't mind being exempt as I have never had to work overtime since I started, and everyone I talk to says they almost never do, and when they do they can usually just take off early the next week if they finished their work.