Overall, rocks are classified into one of three types:
Igneous rocks come from molten magma. Since the Hawaiian islands formed through volcanic eruption, it makes sense that igneous rocks are the most common rocks forming the Hawaiian island chain.
Of course, there are a variety of types of igneous rock grouped together by their mineral compositions (and texture). Different environments of crystallization and magma chemistries result in Mafic, Ultramafic, and Felsic Rocks. The most common type of igneous rock making up the Hawaiian island chain is Mafic rock. Furthermore, the most common type of Mafic rock is basalt.
Igneous > Mafic > Basalt
There are a variety of other volcanic rocks in the Hawaiian island chain, which are covered in detail (with pictures) on the included page.