The answer to that question really depends on what you mean by "cloud."
We're not trying to be pedantic here. The term "cloud" has a variety of rather imprecise usages, and in practice has come to mean just about anything internet-related that isn't encompassed by email, web surfing and social media.
Several home automation companies, for example, promote themselves as cloud-based, but that doesn't mean that the programming for these systems is stored online; the code that turns on your lights is still located on a server within the home. Here, the "cloud" descriptor simply means that the systems can be programmed, monitored, and maintained remotely via the internet. And in some cases, "cloud" is used to mean that you can control your home system remotely via a smart phone or tablet in conjunction with these home automation systems.
In either case, data safety shouldn't be an issue. With such systems, your installer may be able to keep tabs on the stability of your home network, and the devices attached to it, but won't have access to your personal files.
When most people think of the word "cloud," though, they imagine personal data uploaded to off-site servers for remote access. And there are a number of services that allow you to do so with photos, music, videos, etc. This frees up a good bit of hard drive space not only on your home computers or media servers, but also on your phone or tablet, and also allows for more flexible access in and out of the home.
The fact that all of those files are 1) stored on someone else's servers and 2) streamed over the internet to your portable device or your home entertainment system actually raises two security questions: are your files safe on all of those strange servers, and are they safe while zipping over the airwaves?
In both cases, the answer is almost certainly yes. The servers provided by most cloud-storage companies are far more robust, far more secure, and far more likely to be backed up than the hard drives in your home. Furthermore, the encryption used when you access those files remotely ensures that the process is at least as secure as checking your email on your phone or tablet.
Of course, we've all heard stories of people losing photos and music stored in "cloud lockers" — a term used to describe one's one personal slice of storage on a remote server — and it's true that no method of data storage is 100% free from loss or failure. Think of it like mass transit accidents, though: they're far more likely to be reported in the news than personal vehicular accidents and a far greater number of people are likely to be involved at once.
But in the long run, you're far safer on an airplane than you were on the drive to the airport. The same holds true for cloud data storage: when something goes wrong, more people are likely to lose data at once, but in the course of any given day, a far greater number of files are likely irretrievably lost in personal computer crashes and other local accidents.