Evernote is equivalent to one's own notebook so that is the dangerous side of it. It is also very similar to Dropbox.
Dropbox is horrible, it is an open door to storehouses of information. It is designed for personal sharing, although there maybe upgrades to handle security, but out of the box almost anyone can give access to anyone. One of the biggest issues with dropbox, once it is out there you can't get it back. Yes people can accomplish similar things with Skydrive or other Google, yahoo, and email web services. There is a difference between sharing a file to someone and storing important documentation dangerously. If something is easily shared then it is easily shared.
Like no IT department ever had to restore from backup because dave deleted a folder, well that will happen on dropbox. Welcome to Crap Creek, you will not be needing that paddle.
I personally find it ridiculous that people get ticked that their personal information is lost or stolen or unprotected then when it comes to the company they work for it is OK to just give that info out. IT/IS is to protect the life blood of an organization, information. There are other ways to accomplish what some of these applications and services do, that protect the data of an organization. They just might not be free.