You can still download files using chrome when you do a small trick:
Once the download has finished and Chrome tells you that the file you tried to download would be harmful and therefore inaccessible, open up your file browser (explorer or whatever) and navigate to the folder where you tried to save the file to.
You will find a file with the extension ".crdownload" in that folder.
This is the file you've just downloaded.
Just rename that file to it's original filename and extension (Chrome's warning message, which is still in the status bar of Chrome, tells you the original name) and you have your file.
We've seen similar things happening with Chrome in the past already.
Basically Google's idea of treating sites suspicious once there has been malware detected that was available for public access from such sites isn't a bad idea.
In the particular case of download sites this can become a boomerang.
Therefore in the past Google treated download sites different, depending on their ability and will to fight malware distribution.
Mediafire is known to fight malware very hard.
We've faced that in the past too, when e.g. mediafire, for security reasons, decided to treat any self-extracting rar archive as malware.
If you happen to "regularly" (read: multiple times a year) offer "malware" downloads, be it real malware or false positives, mediafire will simply cancel your account.
So the question is: Why did Google suddenly decide to block mediafire?
Well, mediafire is the biggest file hosting site nowadays when you put the porn-hosters aside.
This is big business.
Google never let others run big business alone.
So this move will rather have "strategical" than technical reasons and it wouldn't be too surprising to see some google powered filehosting service pop up soon, or seeing mediafire becoming swallowed by them.
Best regards - Mike