Just bought some Sylvania 27w Compact Fluorescent bulbs.

The note on the back reads:

"Do not use more than 25 lamps per 20 amp. branch circuit."

25 * 27 = 675 watts

675/120 = 5.6 amps.

Is the starting current high enough to require this limitation? Or is it just to accomodate substitutions by incedescent bulbs?

The power factor on those may be quite poor. They usually have inside a small rectifier that converts the 60 Hz AC input to DC and then more circuitry to convert that to a high frequency to drive the florescent tube. So the bulb will draw large spikes of current at the peak of the 60Hz sine wave and nothing in between. This is quite similar to PC computer power supplies in this respect. If the place is fed by 3 phase 120V the neutral will see excessive currents from the harmonics due to the bad power factor. In a house with single phase grounded center tapped 240V(the usual power company feed in the USA) this shouldn't be an issue. Because the timing of the current spikes from bulbs on both sides of the center tap happen at the same time. And thus cancel out on the neutral.