[You know, just to be annoying, I should probably point out that your quote continues "made glorious summer by this son of York". i.e. In context the speech actually implies is "the winter of our discontent" is over.]
Shakespeare's just got so many amazing passages it's hard to choose (I know you said by anyone, but hey, the guy could, at his best, out-write anyone). Personally, my favourite has always been:
"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 turn their currents awry,
And lose the name of action."
Mainly because it seems to apply to so much (not just, you know, contemplating death); it perfectly fits any time you find yourself overthinking or procrastinating to the point of irresolution.
Also pretty much the entire "What a piece of work is a man" speech, not least because it equisitely ends Withnail & I.
[New question with more sequentialness: Is there anything more satisfying than getting a perfect slinky run all the way to the bottom of the stairs?
slinky...spring...geddit? ... Sorry.]