A "sleep" state of VM which is cost wise similar to stop state. The VM wakes up and continues the previous session without rebooting OS.
It is a great feature of Azure to stop costs if the VM is stopped. But shutdown the VM needs close all the running programs and applications in the current session. It will be great if the VM can have a sleep mode which can stop all the costs (or partially). So users can quickly resume the work in the new session without restarting the VM.
This is something that we are evaluating now for a future Azure update.
Sean Feldman commented
We already do something similar with Azure automation, having a schedule to shut VM down and bring it up. Having a Sleep feature would make it much simpler (and better).