I like to be an optimist, always hoping for the best, because, in my opinion, living life otherwise can be pretty depressing. However, as a frugal person, it is also important to be a realist, and prepare for the worst, because if you don't, you can be caught in a lurch that can create a very expensive situation for yourself.
For example, on my trip to the US (wrapping up in a few minutes- in the airport, preparing to board), I decided to “prepare for the worst” and not even consider flying without getting travelers medical insurance, even though I didn't think I'd likely need it- I mean, after all, I'm a healthy woman, even when pregnant, and I rarely ever go to the doctor. But it worked out very well that I got health insurance, despite my being sure I wouldn't need it- because I did end up visiting the hospital while on my trip, and my preparing for the worst saved me and my family thousands in medical bills.
If you're single, if worst comes to worst and you aren't well enough to go to work, often you can scrounge around somehow and manage somewhat until you get better, but even that isn't guaranteed. However, when you're responsible for a family, there is even more pressure to bring in a steady monthly income, because families' expenses are bigger than that of a single person, and the loss of an income, even temporarily, can hurt tremendously. You may want to consider what is known as income protection insurance, which can cover up to 75% of your monthly income when too sick or injured to work. Visit AAMI for income protection insurance.
Additionally, as previously mentioned, getting life insurance for your family can make a huge difference if, worst comes to worst, something happens to the primary breadwinner in the family.
Sometimes, as a frugal person, its hard to spend what seems like excess money on something that seems like an extra, but isn't really necessarily. Yet, it is important to keep in mind that you can be penny wise and pound foolish, and saving money in the short term can cause great problems financially in the long run. It is a good idea to be prepared for things that may happen, even if you don't think it's likely, because “What if?” Would you be able to manage had you not prepared for the worst?
See my disclaimer.