When prince Siddharta went on his quest for enlightenment, he witnessed four kinds of suffering - birth, death, old age and disease. That sobering experience led him to sit under the tree and meditate to find a solution and thus, he became Buddha - The Enlightened One.
You may say - it was just an ancient story, but actually these sufferings concern each and every one of us and there is no way we can avoid it. Still, nobody is asking the serious question - why do we have to suffer? Science is trying to fight diseases, prolong life, preserve beauty but still people are dying, taking birth, getting old and sick.
Bhagavad-gita explains, that birth, death, old age and disease are unnatural to us, because we, as spirit souls are by our very nature eternal, full of knowledge and bliss. Thus making a solution of this “birth, death, old age and disease problem” should be our priority. The solution to this problem is spiritual, not material.
Srila Prabhupada's books, lectures, conversations and letters offer a comprehensive presentation of this essential subject as seen in the Vaniquotes Birth, Death, Old Age and Disease category. An introduction from his books is given below in the following 11 quotes.
It is not a fact that those who are born with a silver spoon in their mouth are free from the material miseries of birth, old age, disease and death. (Śrīmad-Bhāgavatam 4.25.5)
One should always remember that as long as he has a material body he must face the miseries of repeated birth, old age, disease and death. There is no use in making plans to get rid of these miseries of the material body. The best course is to find out the means by which one may regain his spiritual identity. (Sri Isopaniṣad, Mantra 10)
Actually, pure happiness cannot be had within this material world. If we wish to enjoy something, we must suffer for something else. On the whole, suffering is the nature of this material world, and whatever enjoyment we are trying to achieve is simply illusion. After all, we have to suffer the miseries of birth, old age, disease and death. (Śrīmad-Bhāgavatam 4.25.4 )
So there is death even in the topmost planet of this universe, and what to speak of other planets, which are far, far inferior in quality to Brahmaloka, the residing planet of Brahmā. Wherever there is the influence of eternal time, there is this set of tribulations, namely birth, disease, old age and death, and all of them are invincible. (Śrīmad-Bhāgavatam 1.13.19 )
Death is a symptom of the material infection of the eternal living being; only due to material infection is the eternal living entity subjected to the law of birth, death, old age and disease. (Śrīmad-Bhāgavatam 2.3.17)
One should not become a father or mother unless one is confident that he can beget children whom he can deliver from the clutches of birth and death. Human life is the only opportunity to get out of the material scene, which is full of the miseries of birth, death, old age and diseases. (Śrīmad-Bhāgavatam 3.14.22)
Bhagavad-gītā it is stated that man may, by scientific advancement, improve the temporary living conditions, but that he cannot avoid the pangs of birth, old age, disease and death. These are under the control of the Supreme Personality of Godhead through the agency of material nature. A foolish person cannot understand this simple fact. Now people are very busy trying to find petroleum in the midst of the ocean. They are very anxious to make provisions for the future petroleum supply, but they do not make any attempts to ameliorate the conditions of birth, old age, disease and death. (Śrīmad-Bhāgavatam 4.28.12 )
"No one should become a spiritual master—nor a relative, father, mother, worshipable Deity or husband—if he cannot help a person escape the imminent path of death." Every living entity is wandering within the universe, subjected to the law of karma and transmigrating from one body to another and from one planet to another. Therefore the whole Vedic process is meant to save the wandering living entities from the clutches of māyā—birth, death, disease and old age. (Caitanya-caritāmṛta, Madhya-līlā 3.181)
Unless we have a pessimistic view of this material life, considering the distresses of birth, death, old age and disease, there is no impetus for our making advancement in spiritual life. (Bhagavad-gītā 13.8-12)
In the material world the living entity undergoes six changes—birth, growth, duration, reproduction, then dwindling and vanishing. These are the changes of the material body. But in the spiritual world the body does not change; there is no old age, there is no birth, there is no death. (Bhagavad-gītā 15.16 )
The material body is symptomized by birth, death, old age and diseases, but the spiritual body is conspicuous by the absence of those symptoms. (Śrīmad-Bhāgavatam 2.7.26 )