Are the human cerebral hemispheres only connected via the corpus callosum? Are the human cerebral hemispheres only connected via the corpus callosum? Or is there any other structure for interaction between the left and right hemispheres?
The corpus callosum is a massive horizontal white matter tract (commissure) that connects the two hemispheres and it is considered the most important route of communication between the hemispheres. 

However, there are five additional commissures that cross the midline, namely:


Anterior commissure, connecting the two olfactory bulbs and the temporal cortices;
Hippocampal commissure (psalterium), connecting the two hippocampal formations;
Habenular commissure, connecting the habenular nuclei; 
Posterior commissure, connecting the pretectal nuclei, mediating the consensual pupillary light reflex;
Supraoptic commissures (a. Gudden's commissure, or ventral supraoptic decussation connecting the medial geniculate bodies and b. Meynert's commissure, connecting the two suprachiasmatic nuclei*). 



Below figure shows the corpus callosum and the anterios commissure:


Saggital section through the human brain showing the corpus callosum and anterior commissure. Source: Brain Atlas.

*The exact connection of Meynert's commissure I am unsure of. This is the best I could do.