Brightness of three parallel light bulbs
I'm assuming the 120V source is an ideal voltage source.  The overall load resistance increases as you have 2 bulbs in parallel instead of 3, so current at the source decreases.  However, since the bulbs are connected in parallel to an ideal voltage source, the two remaining bulbs see the same voltage as before, hence they pass the same current and dissipate the same power, hence they continue to burn at the same brightness.  

If the voltage source was not ideal - i.e. it has a nonzero source impedance - then the brightness would increase (think of it like a voltage divider - larger R gets a bigger slice of the voltage, more voltage means more current and more power, means brighter bulbs). 

With incandescent bulbs, the brightness is related to temperature, which will be related to power dissipation.  It's actually a bit of a complex relationship - the resistance of the filament will change with temperature, the heat flow out of the filament will also change with temperature, and the "light" out of the bulb is actually black body radiation from the hot filament, and so will change in wavelength and intensity with temperature.