"Sorry, sir. If that subject troubles you"
"Troubles me? What's so damned troubling about not having died?"
Old age was the final stage of a creature's life span. For Humans and Betazoids, this began around their sixties, and for Vulcans, at around two hundred. Those who were in this stage of their life were called old, elderly, elders, or seniors.
In several species, old people were prone to health conditions, which the Kaelon tried to avoid by having everyone on their planet commit suicide when they turned sixty. (TNG: "Half a Life")
Elderly Vulcans ran the risk of getting Bendii Syndrome, but that was relatively rare. (TNG: "Sarek")
Elderly Betazoids could catch Zanthi fever. (DS9: "Fascination")
Kevin Uxbridge was a Douwd who married Rishon Uxbridge and she grew old with him. When he accidentally killed her, he recreated her and the two lived as a simulated elderly couple. (TNG: "The Survivors")
Ves Alkar was a Lumerian who had many dark impulses and negative emotions that he passed on to other people telepathically. As a side effect, these people appeared to rapidly age as well as having the emotions. (TNG: "Man Of The People")
When some genetically-engineered children first reacted to a virus, their immune systems attacked the virus on other people, but eventually started mistaking cells for viruses and killing them, making the person appear elderly. (TNG: "Unnatural Selection")
The elders of Arret and the elderly Drayans appeared as children. Drayan elders also sometimes had memory problems. (TAS: "The Counter-Clock Incident"; VOY: "Innocence")
Data once wondered if he would never be able to marry someone because married couples generally grew old together and he was incapable of growing old. (TNG: "Data's Day")
When Julian Bashir was in a coma, he hallucinated that he was becoming elderly very quickly. When he became conscious again, he noted that he was no longer having negative emotions about turning thirty. (DS9: "Distant Voices")
Mark and Anne Jameson were an elderly couple, but Mark wished to become younger again because in his senior years he had become physically weak due to Iverson's Disease. He took a drug which made him younger, but it killed him because he took too much. (TNG: "Too Short A Season")
Many elders experienced a greying or whitening of the hair. Vori were among those species and used the term "grey" to mean elderly. (VOY: "Nemesis") In an alternate future, Data attempted to look elderly due to having a great many elderly friends by turning some of his hair grey. (TNG: "All Good Things...")
When the Srivani experimented on the crew of the USS Voyager, they made Chakotay elderly. (VOY: "Scientific Method")
The Clown once made Harry Kim appear elderly as a joke on the phrase "you're new [to the area] and they're old, so we have to make you old." (VOY: "The Thaw")
When a group of scientists became afflicted with a virus that made them age rapidly, they spread it to James T. Kirk and his crew, with the exception of Pavel Chekov, whose adrenaline provided a cure. (TOS: "The Deadly Years")
Some, but by no means all, elders became infirm. When an elderly Bolian was infirm, he or she was legally allowed to be euthanized. Kathryn Janeway used this when discussing whether she and her crew should offer Quinn asylum, because they knew he would likely kill himself if they did due to his being bored with immortality and wanting to die. Janeway noted that Quinn was neither elderly, nor infirm. (VOY: "Death Wish") Dalen Quaice was an elderly man who was slightly frail. When he went missing, Beverly Crusher pointed out his frailty and expressed anxiety that he had died. (TNG: "Remember Me") When Jadzia Dax was sparring with an old Klingon friend of hers, she taunted him by suggesting that he'd grown "old and feeble". (DS9: "Blood Oath")
In an alternate future, the Voyager crew had grown old, with the exception of Naomi Wildman and Miral Paris, who were still young adults, The Doctor, who was a hologram, and Seven of Nine, Chakotay, and twenty-one unspecified others, who had died. The Doctor married a woman who he hoped would grow old "gracefully". (VOY: "Endgame")
Sometimes, seniors could develop hearing problems, but that was preventable. (TOS: "The Deadly Years"; VOY: "Endgame")
It was considered polite to minimize effort for seniors. Due to this, the crew of the USS Enterprise-D wanted to transport the elderly Leonard McCoy rather than have him take a shuttlecraft, but McCoy disliked transporters. (TNG: "Encounter at Farpoint")
It was also considered polite to do favors for seniors in particular. This was referenced when Anya, who was a shapeshifter taking on the form of an elderly woman, asked Salia to "do an old woman a favor". Salia said that Anya was no more an old woman than she herself was a leader, but Anya said that Salia was a leader and she herself was older than Salia could imagine. (TNG: "The Dauphin")
Attitudes towards old age varied between species. Humans sometimes feared old age because they associated it with death or with losing beauty, (VOY: "The Thaw"; DS9: "Distant Voices") but Vulcans embraced growing old, because they associated it with wisdom. (VOY: "Alice") Ferengi generally viewed old age negatively because they associated it with loss of stamina and greed. (DS9: "The Nagus")
A robot based on James T. Kirk's memory of Finnegan called Kirk an old man because Kirk was significantly older than him; however, Kirk was actually in his thirties, which was not elderly for a Human. (TOS: "Shore Leave")
Fatal cellular decay was considered normal among elders, but in some cases, it could not be treated. (DS9: "The Storyteller")
According to Kira Nerys, if an old Bajoran was unable to work, the Cardassians might bury them alive during the Occupation of Bajor. (DS9: "Duet")
Rurigan programmed some holographic villagers to be able to grow old and he himself grew old in their village. (DS9: "Shadowplay")
When Kubus Oak was being exiled for betraying his people, he stated that he was elderly and didn't have many years left to live so it would not make a difference if he was allowed to return to Bajor, but Major Kira disagreed. (DS9: "The Collaborator")
A Jem'Hadar was considered elderly at the age of twenty, and was respected. (DS9: "To the Death")