I run VirtualBox on my Fedora system and I don't suffer the problems you're seeing. It could be a problem with VirtualBox but it's also likely that something else was updated at the same time that's causing the boot to fail. A likely culprit is the video drivers.
What do you see when it doesn't boot? Does it get beyond the grub screen? Beyond the filling up Fedora logo in the middle? Does it get to where you expect the log-in screen to appear and then go all black? Can you actually describe what it does that's different to a normal boot? If the fedora logo appears and starts filling, what do you see if you press 'esc' and flip to the service startup screen?
Can you open a text console after it's 'failed' to boot? (You do this by waiting for the boot to complete as far as it can then press CTRL-ALT-F2). If you get a command prompt you know your video drivers have failed.
The last resort would be to get into single user mode (that mean editing the kernel boot line in grub - something we can talk you through if you need to) then uninstall the last set of updates using yum. You have a yum log telling you exactly which packages you installed last in the /etc/log/ directory, which you'll need root privilege to read.
@kwoodle I don't have any problems with running VirtualBox on my Fedora 20 laptop, don't give up.
can't be related , VirtualBox doesn't affect boot process