For high frequency designs and good decoupling I like lots of ground plane, so my design for a switching regulator, for example, had ground pour on the top middle, and bottom layers, tied together with numerous vias. That way the surface mount decoupling capacitors, which were mounted close to the power pins on each IC, are connected directly to the ground plane. To improve the decoupling effect of the capacitors I also tried to run the power trace directly through the other mounting pad of the cap, instead of using a T connection, wherever possible. That minimized trace inductance on both sides of the decoupling capacitor to essentially that of the capacitor package, which maximizes the decoupling ability of the cap. I did make the power traces wider than the signal traces to minimize trace power line impedance.
For low frequency or audio type circuits putting power on one layer and ground on the other should also work fine. The capacitance between the two layers will act like a small decoupling cap from power to ground.