For those with are running Ubuntu Trusty as an OpenVZ container (eg. through proxmox), you should consider to upgrade rsyslog. Indeed, rsylogd, as provided in the default Ubuntu Trusty repository, has a bug resulting to a full CPU consumption.
You can update rsyslog as follow:
1. Add the following repository in your /etc/apt/sources.list
2. Update the rsyslog package
Once done, you should comment the repository in your /etc/apt/sources.list to prevent any other package to be updated.