Jabaar - what we did when our dc were small (they're teenagers now) is make sure we built up a support network so there were different options for emergency childcare.
We didn't have a lot of support from family either, so this involved things like swapping favours with friends and sometimes employing nannies from the children's nursery to help out at our home when they were on days off from the nursery.
And dh and I would take turns to look after the children when they were sick.
Admittedly it helped a lot that we both worked shifts and weekends, so our time off in the week was more flexible and so did some of our friends.
We still exchange favours - e.g. giving lifts, having teenagers to stay while their parents go away.
ssd - yes, you could be sacked if you ended up being more unreliable than the business could tolerate, as flowery says.
Funnily enough, we've recently been on the receiving end of colleagues having time off for dependents - with me and dh having to take on extra work and change hours at short notice. We don't mind as we know what a pita it can be, but it is disruptive and I can understand why colleagues without children can sometimes resent it.