Loose laminations will make it worse but all transformers hum due to magnetostriction.
Transformers will also hum
much louder if the mains voltage has a DC offset. This is especially an issue with toroidal transformers, where a seemingly small DC offset can cause the core to go into saturation (which blows the fuse due to the rapidly dropping inductance of the primary winding, which in turn leads to a rapid increase in primary current).
Transformers in metal cases (e.g. sheet metal) will also hum louder than ones in plastic cases since they essentially use the metal case as a loudspeaker membrane (bending it marginally with their magnetic field). Increasing the distance to the case will reduce the hum in that case.
Another cause of hum can be filter capacitors, this hum typically sounds much "brighter" (more higher frequency content). This is caused by electrostriction in the caps. Sometimes it's also caused by magnetostriction in the transformer due to the rapid current increase when the filter caps are charged (100 times a second).
And at very high currents even the rectifier diodes can start to make noises...