As an IT person for over twenty years, I still pain at this cloud presence. Who owns your data? Google, Amazon, Microsoft?
What, specifically, are you afraid will happen?
I can see being worried about handing your business data to a service provider who may be a competitor, but are you actually competing with any of these? And would they really get enough value from looking at your data to justify the immense damage to their business if they were caught spying on customers in violation of contractual obligations? Not likely. I suppose I could see Wal-mart refusing to host their data on AWS because there's a clear competitive conflict, and Wal-mart is big enough that Amazon might want to spy on them, but those cases are pretty rare, I think.
If your concern is about data loss if the provider goes belly up or has severe problems (e.g. a data center burns to the ground) then (a) your fears are pretty misplaced with respect to AWS, Azure or GCE, and (b) you should be keeping backups regardless of whether you're running your own systems or using a provider. If your concern is about downtime, your fears are really misplaced. The big cloud providers are much better at that than you are.
I know a number of small and mid-size companies that have never operated their own data centers, or even had colos, and are extremely happy with the way that works. It makes them able to respond to changes in business much more quickly and keeps their overhead low, especially during the early phases. Sign up a huge new client and need to double your capacity? Log on and fire it up (assuming you've architected for scalability). No need to worry about floor space or purchase orders or installation schedules. Lose a huge client or find an optimization and need to cut capacity by 30%? Log on and shut it down. No need to figure out what to do about the idled equipment or floor space. These companies find it's much better to stay focused on what they do well, writing software and selling services, rather than staff up big organizations to manage data center operations.
One significant (~600-person) and quite profitable SaaS company I know doesn't own *any* computing hardware. Their computing equipment is completely BYOD, employees use their own laptops, tablets and phones (with reimbursement, so I suppose their accountants might argue they own some stuff, technically). When they had to move buildings recently (due to growth), they simply leased a new building and told everyone (those who don't telecommute) to show up at the new location the next week. The new building had cubicles and wired and wireless Internet in place (w/redundant providers), all part of the lease. They did contract some movers to haul boxes of personal items from the old building to the new one, including developers' large monitors. The CEO likes to joke that he could move the entire company to a beach-side resort in Belize and they could all continue working without the slightest interruption, as long as the resort had good Wifi.
That's a bit extreme, and there's no doubt that that level of flexibility isn't free, but it's not as expensive as you might think. Moreover, if your workload is very static, and your IT department is solid and smooth-functioning, and labor costs in your area are low, it will cost more to pay a cloud provider than to do it yourself. Or if you have particularly-sensitive data to manage (and actually know how to manage it... something that is *rarely* true in my 15 years' experience as an IT security consultant), you may need to have your own hardware. But for many, many companies, the cloud is cheaper, faster, more flexible and more secure.