Voyager 2 was at the edge of the solar system when JPL diagnosed and corrected a single bit error that caused it to return garbage data.

http://www.jpl.nasa.gov/news/news.cfm?release=2010-151

That is beyond amazing.

Once you build an "over the air" upgrade capability and a fail-safe mode (unlike my Android phone, thanks for nothing G & S) you can do it

But the software, as far as I know, is very modular, so this could be only an upgrade of some modules

Edit: by RTFA this looks more like a replacement rather than an update, like, making usage of all the landing software space since this is not needed anymore.

Spirit and Opportunity were upgraded as well.

When they took off, the autonomous navigation wasn't even close to complete. They pushed that software once the two Rovers were already on Mars.

(I was working on the Rover team at the time)

I was gonna say the only reason I can think of to not load the software before it takes off is because it isn't finished yet. I'd imagine memory is pretty small/inexpensive even if it has to be specially fitted to get blasted across the solar system and work next to a nuclear power plant.

Cassini launched before they had finished writing the software needed to enter and tour the Saturnian system. They finished writing it while it was en route and uploaded it prior to arrival.