As with most other areas of health, the best course of action is to lead as healthy a life as you can.
By the time you reach old age, the lifestyle decisions you took when you were younger may be having an impact, such as with cancer, diabetes, breathing problems or liver damage. However, even if you have any of the above conditions, if you eat and drink healthily and you maintain as active a lifestyle as you can, you can maintain a high level of physical health and mental wellbeing.
Being socially active is a great thing to do as you enter your more senior years. A good social life can keep you entertained and active and can provide great happiness, as well as being a means of support during any difficult times.
If you aren't physically able to do too much exercise then your diet is even more important, as you won't be burning off as many calories as somebody who is more active. Also if you can't get about as much, it is crucial that you keep you mind alert and busy, whether by doing crosswords, taking part in quizzes etc. You can also use technology such as Skype or Facetime for a more personal way of keeping in touch with your friends and family.
Most importantly, if you aren't well, then make sure that you get the appropriate treatment when you need it. Some elderly people can be reluctant to contact any medical services because they feel they are causing trouble. It is far more important to get yourself checked up and for a problem to be detected early, rather than to try to cope and allow the problem to grow. If in any doubt, get checked out.