Bzzzt! Wrong answer, try again. They are not good for anything remotely resembling production. Since your production should try and closely resemble everything else I'd say they are not good for anything at all. The tag line is "Cloud computing, designed for developers." They should be even more careful about good practices and sound design keeping in mind the kind of customer they are trying to get. Over the years they have done anything but that.
I run my personal server on DigitalOcean and it has been pretty good. At work we run a series of tier-2 services on DO and it's been great for our use cases. We used to run a cluster of 100 machines there and it was stable and cheap.
I realise it's very simple, and that isn't good for a lot of production services, but I don't understand the hate?
Actually your DSL is probably more secure because it wasn't designed by complete muppets. Who thought it a good idea to put everyone on flat Layer 2 network. Remember the time they were handing out block devices without scrubbing. How is the new Ceph backed block service. What's the p50 latency? What about p90?
Professional non-trivial usage should be on AWS/Google/Azure/SoftLayer.