[Update:
VirtualBox 4.1.20 and later are now completely compatible with Mountain Lion and this jiggery-pokery is no longer needed
- FB]
Apple released Mountain Lion (Mac OS X 10.8) late last week and a few people are stumbling over installing VirtualBox on it, so here are a few tips:
At the time of writing, the current version of VirtualBox is 4.1.18. Strictly speaking, this is not commercially supported, but VirtualBox users tend to be an intrepid and gung-ho bunch, and will try to run it on Mountain Lion anyway. They'll download VirtualBox and run the installer by clicking on the VirtualBox.mpkg icon:
...and get a message like this:

This will happen if you are using the default Security settings of Mountain Lion for downloaded applications, which probably look like this:
To get VirtualBox installed you can either:

...which now has an Open button. Clicking on this will get VirtualBox installed too.
HTH someone out there.
-FB
P.S. You can expect to see a "Fully Supported" version in the not too distant future