Internet Button
Whilst looking for something I could do with an ESP-01 and sleeping/batteries, I found this, which itself was inspired by this (which I couldn’t get to work!)
Essentially you power on the ESP-01 by pressing a button. Now whilst that sounds lame, the clever part is that once its on, you can do whatever you like e.g. post to a website, and then turn the unit back off (by setting GPIO2 and CH_PD low) until the button is pressed again.