That's a pretty vague question. It all depends on what you mean by "safe", what you're storing, and what goal you're trying to accomplish.
Are they safe as in "am I definitely the only one with access to the account?" That answer would be no, every major consumer cloud storage player has had a data breach or major security flaw discovered in the last few years.
Are they safe as in "do they meet federal regulatory compliance for my industry?" That depends on the service, but 99% of them do not meet the requirements for things like HIPAA/HITECH and SOX and you legally cannot store protected data on them.
Are they safe as in "do they use encryption for transmission and file storage?" Again, depends on the service but most do not.
Are they safe as in "are they going to work with law enforcement should they request access to my data?" Then again, the answer is no. They'll give you up in a heartbeat, so I wouldn't store my pirated music collection or secret terrorist plans on Dropbox
That being said, it's not like there's no value to these services as long as you understand that your data, not the service, is the real product here. They're giving you 5GB for free because they're absolutely datamining the stuff you have up there and selling it to marketing and demographics companies. You have no expectation of privacy and if you read the fine print once the data is uploaded they can do whatever they please to it. They're great tools for sharing quick notes or backing up your family photos. If you're looking for a free vault for your illicit materials, you won't find it here.