First off, there is a difference between a reboot and a stop followed by a start - things always persist across reboots.
After that it depends on the volume type. Instance store volumes do not persist across stop/start, but EBS volumes do. EBS volumes will hang around after an instance is terminated too, unless the destroy on termination flag is set.
Whether your root volume is EBS or instance store depends on the AMI you started the instance with. Amazon do seem to have been encouraging people to use EBS.