这句话出自莎士比亚的《哈姆雷特》第三幕第一场哈姆雷特著名的独白“To be, or not to be: that is the question:......”
当时哈姆雷特为复仇装疯，对一切产生怀疑，却又优柔寡断，矛盾重重。
关于这句话有多种译法，而且还有争论。较常见的是朱生豪的译文：“生存还是毁灭，这是一个值得考虑的问题”。
其它译文：
梁实秋：死后是存在，还是不存在，——这是问题。
卞之琳：活下去还是不活，这是问题。
许国璋：是生，是死，这是问题。
王佐良：生或死，这就是问题所在。
方 平：活着好，还是死了好，这是个难题啊。
孙大雨：是生存还是消亡，问题的所在。
裘克安：活着，还是不活了，问题就在这里。
生存还是毁灭？这是个问题
等等
剧本原文：(
http://www.artofeurope.com/shakespeare/sha8.htm)
To be, or not to be: that is the question:
Whether 'tis nobler in the mind to suffer
The slings and arrows of outrageous fortune,
Or to take arms against a sea of troubles,
And by opposing end them? To die: to sleep;
No more; and by a sleep to say we end
The heart-ache and the thousand natural shocks
That flesh is heir to, 'tis a consummation
Devoutly to be wish'd. To die, to sleep;
To sleep: perchance to dream: ay, there's the rub;
For in that sleep of death what dreams may come
When we have shuffled off this mortal coil,
Must give us pause: there's the respect
That makes calamity of so long life;
For who would bear the whips and scorns of time,
The oppressor's wrong, the proud man's contumely,
The pangs of despised love, the law's delay,
The insolence of office and the spurns
That patient merit of the unworthy takes,
When he himself might his quietus make
With a bare bodkin? who would fardels bear,
To grunt and sweat under a weary life,
But that the dread of something after death,
The undiscover'd country from whose bourn
No traveller returns, puzzles the will
And makes us rather bear those ills we have
Than fly to others that we know not of?
Thus conscience does make cowards of us all;
And thus the native hue of resolution
Is sicklied o'er with the pale cast of thought,
And enterprises of great pith and moment
With this regard their currents turn awry,
And lose the name of action. - Soft you now!
The fair Ophelia! Nymph, in thy orisons
Be all my sins remember'd.
朱生豪译文片段：
生存还是毁灭，这是一个值得考虑的问题；
默然忍受命运暴虐的毒箭，
或是挺身反抗人世无涯的苦难，
通过斗争把它们清扫，
这两种行为，哪一种更高贵？
......
参考资料：http://www.eywedu.com/Yilin/yiwen/content/yiwe20080304-3.html