'nightfall' is also very good, both the short and novel version.
It may have influenced Vernor Vinge's Deepness in the Sky portrayel of the civilization of the intelligent spider creatures who hibernate through the "Deepest Darkness" of their variable sun's long "off" periods where their civilization falls apart.
One of the comments in the older threads mentions how the Multivac represents the opposite of what we got today, because we have so many computers running at the same time (phone, laptop, tv, and tablet currently around me, for instance).
I can't completely agree. Although all these devices might work by themselves. But they are not complete. Each of these machines is currently running software that actively connects one or the other cloud service. Isn't what we have pretty much that Multivac thing? It's not a single big blob somewhere on this planet, but this just makes it way bigger.
Thank you for posting it. I first reading this story as a teenager. I remember it having an impact on me in a way few stories do. I have re-read it many times since then and it can still take my breath away every time.
I came here to say precisely this. I didn't even know Asimov at the time; I started with some of Arthur C. Clarke's stuff). Years later I had to hunt it down to find it again, and that resumed my love affair with Asimov.
It's hard to believe he was 21 when he wrote Foundation. Easier to believe when you see how profound he could be in such short bursts as with OP.
http://www.thrivenotes.com/the-last-answer/