All depends on who you are and what mode of philosophy you follow, really! But that would be a cruel answer, so let's go ahead and look into some of it. I've been reading quite a bit of Seneca lately, and he offers some wonderful opinions on the matter.
Some quick background on Seneca before we start - if you want to get straight through to the actual "thoughts on death thing," feel free to skip this paragraph! He was a Stoic philosopher who's moderately well known today (I've seen some cherry picked quotes of his on Facebook and such) due to his letters - many of which we still have today. In these letters to his friend (Lucilius), he grouches a lot, but has some really fantastic discussions that give a glimpse into daily life and thought in the Roman world. Seneca himself was pretty high on the Roman food chain - he was Nero's tutor, and helped govern the Empire while Nero was still young. Nero eventually killed him, though, so there's that. Anywho - on to Stoic philosophical thought about death.
A couple of letters that essentially encapsulate this entire question are his 21st letter to Lucilius - on "creating a lasting monument" - and his 24th- on "despising death." In the former letter, he writes about how people are so easily forgotten after their deaths. In the latter, he discusses not only the wider view of death, but also his own and why he thinks that the wider view of death is bullshit. I'll start with letter 21, particularly this passage (Note - these translations are not quite beautiful, but they get the point across pretty nicely):
Allow me to mention the case of Epicurus. He was writing to Idomeneus and trying to recall him from a showy existence to sure and steadfast renown. Idomeneus was at that time a minister of state who exercised a rigorous authority and had important affairs in hand. "If," said Epicurus, "you are attracted by fame, my letters will make you more renowned than all the things which you cherish and which make you cherished." Did Epicurus speak falsely? Who would have known of Idomeneus, had not the philosopher thus engraved his name in those letters of his? All the grandees and satraps, even the king himself, who was petitioned for the title which Idomeneus sought, are sunk in deep oblivion. Cicero's letters keep the name of Atticus from perishing. It would have profited Atticus nothing to have an Agrippa for a son-in-law, a Tiberius for the husband of his grand-daughter, and a Drusus Caesar for a great-grandson; amid these mighty names his name would never be spoken, had not Cicero bound him to himself. The deep flood of time will roll over us; some few great men will raise their heads above it, and, though destined at the last to depart into the same realms of silence, will battle against oblivion and maintain their ground for long.
Again, while this one doesn't directly address death, I thought it fit in rather nicely with the wider idea of "being remembered." Essentially, as he notes, there are many people who would be utterly forgotten by the sands of time if not for some few being saved by being included in letters. He uses the example of Atticus; another easy example is that of Lucilius himself, of whom we know only what Seneca wrote. In the letter, however, he notes one of the most truly notable things about death: Those things which each man leaves behind, and how men who are remembered are essentially immortal.
Anywho, next letter, which addresses things a bit more directly! I can't quote this one, because it's just that long (it's slightly over the 10k character limit in itself, which is a pain in the rear - if you want me to quote it in a later comment, I'll be happy to), but I really encourage you to read the whole thing. It's incredibly beautiful and I won't be able to do it justice through my writing here, but hey, I'll give you a vague idea. Letter 24, same disclaimer on the translation.
There are varying degrees on which a person may consider death, which hold true to the modern day as much as they did 2000 years ago. Then, as now, most people feared death - yet, in a truly Roman fashion, they looked up to those who embraced death, rather than allow themselves to be dishonoured. Embracing death isn't necessarily about a person being suicidal - it was about a man who had the option to live in disgrace, but rather chose the path of death. Seneca lived in the First Century CE - these letters were written during his retirement, between 62-65 CE. One of his favourite notes describing this is described in this passage from the aforementioned letter:
"Oh," say you, "those stories have been droned to death in all the schools; pretty soon, when you reach the topic 'On Despising Death,' you will be telling me about Cato." But why should I not tell you about Cato, how he read Plato's book on that last glorious night, with a sword laid at his pillow? He had provided these two requisites for his last moments, - the first, that he might have the will to die, and the second, that be might have the means. So he put his affairs in order, - as well as one could put in order that which was ruined and near its end, - and thought that he ought to see to it that no one should have the power to slay or the good fortune to save/c Cato. Drawing the sword, - which he had kept unstained from all bloodshed against the final day, he cried: "Fortune, you have accomplished nothing by resisting all my endeavours. I have fought, till now, for my country's freedom, and not for my own, I did not strive so doggedly to be free, but only to live among the free. Now, since the affairs of mankind are beyond hope, let Cato be withdrawn to safety." So saying, he inflicted a mortal wound upon his body. After the physicians had bound it up, Cato had less blood and less strength, but no less courage; angered now not only at Caesar but also at himself, he rallied his unarmed hands against his wound, and expelled, rather than dismissed, that noble soul which had been so defiant of all worldly power.
Yeah, he was plenty snarky :D That's the kind of thing that the Romans admired, though, when it came to despising death. Seneca straight out says that, although a man shouldn't fear death...
The grave and wise man should not beat a hasty retreat from life; he should make a becoming exit. And above all, he should avoid the weakness which has taken possession of so many, - the lust for death. For just as there is an unreflecting tendency of the mind towards other things, so, my dear Lucilius, there is an unreflecting tendency towards death; this often seizes upon the noblest and most spirited men, as well as upon the craven and the abject. The former despise life; the latter find it irksome.
Self explanatory :) Hope that answered your question! Feel free to read through the letters themselves - not only are they super quotable, but they're absolutely fascinating reads. Feel free to ask if you have any more!