Docker
Docker is probably the single most popular container service. It was released as an open source project in March 2013 by dotCloud, Inc., and since then, major players like Red Hat and Microsoft have started collaborating with it.
From a security standpoint, Docker can be considered very safe even if it's a new technology, since it does not manage a majority of its security features. Instead, these are demanded to the Linux Kernel, which uses well-tested modules, such as cgroups, SELinux, and AppArmor.