Smoothing rectified voltage
You can rectify and filter the voltage to a somewhat higher voltage, with a smaller capacitor and correspondingly higher ripple, then use a regulator to reduce the ripple. That is probably the most common approach.

If you don't need the voltage regulated, another possible circuit is a capacitance multiplier. Again, you throw away some power in an active device to reduce the ripple, but in this case you're not stabilizing the output voltage against changes in input voltage or load current. 

But a few thousand uF electrolytic capacitor is not very large (for example, 18mm diameter x 20mm tall for 4700uF/16V) compared to the power transformer you would need, so I don't see why there would be an issue. 

Even with a regulator or capacitance multiplier you will need a capacitor of fairly large size because it has to store enough energy to supply 0.5A during the relatively long period between AC peaks. 

If you have a 12VAC transformer you would get about 16VDC out assuming a full-wave rectifier, and the transformer would need to be rated at about 13VA or 800mA. A 4700uF capacitor would yield 0.01s * 0.5A/4.7mF = 1Vp-p ripple, assuming a 50Hz mains. 

If you added a linear regulator  you'd get 12V with a couple watts dissipation in the regulator at 0.5A (so a heat sink). That might not be enough to guarantee it wouldn't drop out and start passing the ripple under worst-case conditions, depending on the dropout voltage of the regulator and your specification for mains tolerance, you'd have to do a careful design to be sure. A switching regulator could run much cooler, but that means more complexity and another much smaller filter capacitor. 

Finally, what most modern electronics does is rectify the mains, use a capacitor of similar physical volume to a 2200uF or so capacitor, but much less capacitance and rated for perhaps 400VDC. The mains is rectified and filtered, and chopped at tens of kHz, passed through a much smaller and lighter transformer, and regulated with a closed-loop feedback scheme. The amount of material required is much less, the mass and volume is much smaller, efficiency is high, and regulation can be pretty good (and  you can add a small linear regulator after it to further reduce it). The noise can be a problem in a few applications, but in most it's almost ideal.