Yes, the power adapter is fully isolated, but the device that is powered by it may have exposed conducting parts, that may carry a dangerous voltage in case of malfunction. Or, may carry a low but annoying voltage due to normal leakage currents. Galvanic isolation cannot completely avoid capacitive leakage currents.
(Actually it can, with a grounded screen between the windings, e.g. for surgical devices, but obviously this needs the ground wire.)
I don't understand why other answers pay so much attention to the inner workings of the switched mode power adapter. Evidently, every design features galvanic isolation. Before, a 50 Hz (US: 60 Hz) two-winding transformer. Nowadays the transformer works at a much higher frequency, and is accordingly smaller and ligher, but that is not the point.
Note that the ground lead is just an optional thing. It only does any good if using a grounded wall outlet. It does nothing on an ungrounded wall outlet. Ungrounded wall outlets should only be used where you won't be instantly killed when touching live voltage, such as a living room with a wooden floor instead of a concrete floor. But nowadays I am seeing grounded outlets virtually everywhere.
Note also that the outlet earth may not completely eliminate the annoying small voltage on your device. That ground is designed for safety, to blow the fuse before you get electrocuted, but not for guaranteeing zero volt. The ground wire resistance, and also inductance, may still be significant. For example, I often experienced 'tickling' voltages when handling the VGA cable on the 17 inch CRT monitors, even on a grounded outlet, probably because of the capacitive leakage from the internal 10.000 volt for the tube. (17 inch? those monitors were so big, expensive and heavy. Now we have cheap lightweight 23 inch, 27 inch, UHD, .... )