Any visible planet or asteroid would. So some stars would also appear to blink out, but those would take longer to blink out. So the moon would go after 8 minutes, Jupiter would take 43 minutes to stop receiving light, and another 35-52 minutes to disappear for earth depending on orbital locations.

Presumably we would get something on radio/tv/internet from the side facing the sun once they realized it, that of course being only if they hadn't already been eradicated by a horrific shockwave caused by whatever event caused the sun to vanish before they had a chance to report what they saw, because supernovae tend to travel at very close to the speed of light, so there wouldn't be much time for them to react.

And if this is a supernova, you might just have time to grok what happened before the planet was obliterated under your feet from the shockwave.

So I guess... chances are we would just barely understand what happened before we were gone.