  Motivated by recent numerical results, we study the quantum phase transitions
between Z_2 spin liquid, Neel ordered, and various valence bond solid (VBS)
states on the honeycomb and square lattices, with emphasis on the staggered
VBS. In contrast to the well-understood columnar VBS order, the staggered VBS
is not described by an XY order parameter with Z_N anisotropy close to these
quantum phase transitions. Instead, we demonstrate that on the honeycomb
lattice, the staggered VBS is more appropriately described as an O(3) or CP(2)
order parameter with cubic anisotropy, while on the square lattice it is
described by an O(4) or CP(3) order parameter.
