What happens when you work, and your child gets sick?

This question is sparked by TinyFaery’s question about parents with children getting preferential treatment at work with respect to time off to care for sick children.

What would you perceive as an ideal solution for working people with sick children? Should they bring them into the workplace when school or daycare won’t take them? Should work pay for someone to take care of sick children so the parent could come to work (one place I worked did this)? How exactly should a baby with a fever of 104, a puking toddler, or a teenager that just had their tonsils out, being cared for if both parents work, or their parent is a single parent? Should a grandparent be required to miss work?