I think it's normal for us to ponder the what-ifs of our life as we age. You don't give your age range but perhaps these tips will help. (I am completing my Master's in Family Studies, dealing with family crisis and life changes.)
1. Consider creating a fund for your golden years (with today's economy that may be tough right now but if you give up a cup of store bought coffee/ bottle of cola daily put the money in a jar)
2. Write the pros & cons of being in a nursing home
3. Type up a "what my family needs to know" statement giving details of how you wish for your finances to be handled, living will etc. (UPDATE REGULARLY and have it NOTARIZED)
4. Talk over your concerns with your children, (if they are old enough to understand and converse with you on this topic.)
5. Talk to your spouse about how each of you will manage if health problems arise
6. Continue to look for ways to add to your nest egg, (401K's, IRA's, Life Insurance that pays premiums)
7. Seek spiritual guidance (Christianity, Judaism, Buddhism, Tarot Cards) whatever your belief

Start optimizing your health; exercise, develop good health standards. Perhaps you need to develop a hobby or become active in your community to help take your mind off this topic occasionally.

But on the other hand living in the "Old Folks Home" won't be all that bad...
1. 3 meals a day prepared and brought to you on a tray (and snacks!)
2. Neighbors who love to have you visit (and often)
3. All the TV you care to watch
4. Doctors make "house" calls
5. No more dirty dishes
6. No more laundry