My Nexus 7 had been performing without any issues, however, I locked the screen by pressing the power button as usual and then tried to turn it on several hours later but it was unresponsive.
How can I fix this?
I've managed to deal with this problem by performing a "soft reset".
Hold down the power button for around 30 seconds, the device should start a soft reset (i.e. you don't lose any data/settings etc.) and reboot.
For those that tried the soft reset to no avail: some tablet covers have magnets in them used to toggle the screen on and off. If your cover is poorly made, it may trigger the screen to turn off at inopportune times, e.g. when you have it folded back like a book cover and it's turning your screen off as soon as you get past the lockscreen.