Yes, when I'm too impatient with waiting for the stupid things to charge up. If there was an easy way to select your ready to fire superweapons it would be a different story, but against the CPU I often find myself putting it on autocast during dull moments. However, you may want to take it off for the culture cannons and Kosturas as they can give a combat boost or a quick re-enforcement route in addition to their main effect, which you might want to make sure you have avaliable in close games.

Micro? I keep seeing that word but I do not know what it means. Well I do know what it means, I do not know what you are refering too in game.

What about any of the other features in the game that do not automatically get autocast, like the scout frigates explore ability?

Goafan, you can put your superweapons in a numbered hotkey just like any other ships or buildings, and tab through to see which are ready. 

I've used auto with the culture cannon.  In a huge multi-star scenario where you have two dozen of them firing at once, you don't care where so long as they actually are firing.  However, if I only have one or two I'd certain choose my targets carefully.

Usually I use auto-cast in huge fleet battles where I just don't have the capacity to manage my own units.  Setting a mothership to autocast shield restore is a perfect example.  There are just too many abilities, however, which the auto-cast AI royally messes up for any systematic use of the feature.