There is a big difference between a plumbing problem and a plumbing emergency. A plumbing problem is a bubbling toilet or a slow drain, while a plumbing emergency usually involves water gushing all over the place, such as from a busted pipe, or contaminated water backing up into your home from a sewer backup.
Depending on how handy you are, you might be able to handle the problems on your own, but the emergencies are a different beast altogether. You probably will need the help of a professional.
So what could prove to be a plumbing emergency? One major issue is a broken water line which would leave you and your family without water until it is fixed. It could happen spontaneously when the ground shifts due to changing seasons, or you might be digging in the wrong place. Either way, you need help, and you need it fast.
Sewer backup is also an issue that will mess your life up in a bad way. It could be because of roots in the sewage line or some other type of clog, but they will usually be stubborn clogs that prove hard to get to.