Seems like all the simpler Lie algebras have a use in one or another branch of theoretical physics. Even the exceptional $E_8$ comes up in string theory. But $G_2$? I've always wondered about that one.
I know only of one false alarm in the 1960s or 1970s before $SU(3)$ quark theory was understood, some physicists tried to fit mesons into a $G_2$ representation.