With many questions in life the answer to this question is “It Depends.” The first factor one needs to evaluate is your level of wealth. The more you have the more you have to protect. If you are young and just starting to build your nest egg, your greatest risk is most likely becoming disabled and not being able to earn a living. In this case you should be focused on disability insurance. If you have begun building a nest egg and have investments assets in excess of $400k, you should probably start thinking about long-term care insurance regardless of your age.
Second factor to consider is your age and particular family circumstances. Some might argue that you do not need to look into this until your 50s or even your early 60s. I disagree. Most married couples want to ensure that they and their spouse can maintain a certain standard of living regardless of what happens to them. While most people do not need assistance with normal activities of daily living until later in life, please raise your hand if you know of someone who has become chronically disabled before the age of 65. While not likely that someone in their 30s or 40s would need long-term care I always caution people to not treat the highly unlikely as impossible. If you are married and have built up enough assets, you should consider long-term care insurance.
Third factor to consider is children. Do you want to leave something for your children? Do you want to be a burden to your children? While everyone has different thoughts on this, most folks I meet do want to leave something for their children and do not want to be a burden. Even a modest long-term care insurance policy can assist in protecting your assets and relieving some level of family stress if the times comes when you may need some assistance.
Finally, your current health is a factor. For those who are young and healthy, you may convinced that you will always be that way. There are those who know better. The best time to consider this type of insurance is before you develop medical conditions that can cause you to be denied this coverage.