In DC circuits, if I have a device that gets switched on and has a large inrush current, I can just put a large charged capacitor near the power switch (parallel to the device) to source the surge.
You could also use a slower switching time, or ramp-up the power to the thingy which has huge inrush current. DC-DC converters usually have a slow-start feature, in order to startup with the load has lots of decoupling caps.
Is there an AC circuit equivalent to my DC capacitor/in-rush scenario?
Well, I've seen it in audiophile amplifiers, because these guys like to put enormous values of capacitance after the rectifiers, thus when you turn the amp on, the fuse blows, which is kind of a bummer.
There are two ways to do this: the brutal way and the smart way.
The über-brutal way is a NTC thermistor in series with mains. It has lots of resistance when cold, and low resistance when hot. Thus it limits inrush current, but only when it's cold when the power switch is pressed.
The brutal way puts some resistors in series with the transformer primary, which limits current when charging the caps. A few seconds after power is switched on, a relay closes and shorts the resistors.
If someone cycles the power button ten times in a row on the two previous circuits, something may catch fire. YMMV.
The smart way uses a triac dimmer, just like a halogen dimmer. It slowly ramps up the voltage on the transformer primary, by advancing the phase angle. So the caps charge slowly. But you need to design the triac dimmer properly for the transformer load.
Modern power supplies (like PC ATX)