What percentage of people end up in nursing homes in the world?

The number is rising, because of the tragic increase of dementia in the world's population.  However, I don't know the exact percentage.  

Not that high

Most countries have no such thing as nursing homes

In most countries the elderly are cared for at home

Less than 1%.  Outside of America it is common culture for family's to care for their elderly themselves (and there aren't any nursing homes as a result).  In America, about 50% need to stay in a long term care facility at one time in their life if they reach 65 years old or older (10-20% don't make it to 65).  But only about 20% of old people die in nursing homes.  60% die in hospitals, 20% die at home.

Very low when you take into consideration the number of people who die from birth through their 60s or so.  Then you're just dealing with a small percentage who are much older and end up there.