The bulbs will only appear brighter if the available current to the system is not limited. In that case, the series bulbs will have a lower voltage across each individual bulb and they will appear dimmer. If the power input to the circuit is constant then the total wattage output from all bulbs is also constant and the bulbs will all appear the same (assuming the filaments for the bulbs are all identical resistance).
In a typical simple circuit, the power source will be a battery which attempts to hold a constant voltage across the circuit. In this case, the voltage across the bulbs in parallel will be equal to the voltage of the battery and the current through the bulb will be defined by V = IR where R is the resistance of the filament. This means more current (and thus more power) will be drawn from a battery into the parallel circuit than a series one and the parallel circuit will appear brighter (but will drain your battery faster).