A number of answers here on this Stack Exchange argue that containers are inherently insecure and one should never run untrusted code in a container, let alone run a container built entirely by someone else.
And yet, there are a number of companies currently offering AWS-style VPS services that use containers instead of virtualization.
Of course, unless you run your own private datacenter with armed guards and don't connect it to the internet, no VPS or rented server is perfectly secure. For containers to be relevant, the possibility of attack doesn't need to be zero, it just needs to be sufficiently small compared to the attack vectors of alternative services.
So the question is: just how safe can containers be? Are there container systems (if so, which ones) which have no known exploits currently, and for which exploits are likely to be fairly hard to craft?
And one specific aspect of the question: At worst, is there any container system in which running an untrusted container can be considered as safe as running un-containerized code as an unprivileged user?