SSIS Error opening packages / MSXML corruption

This morning, I went to open some packages that I had been working on last week, and was surprised (and a little panicked!) to get an error saying that the package couldn't be opened. After clicking OK, the package seemed to be fine - in the Control Flow - however my data flows were empty! Looking at the message in the Error tab scared me even more!

"Unable to instantiate XML DOM document, please verify that MSXML binaries are properly installed and registered."

After some digging, I found that you can repair the binaries by going into 'Add/Remove Programs', clicking 'Change' on the 'MSXML 6.0 Parser', and selecting the 'Repair' option (shown below). After doing this, the packages opened just fine.