  We report giant Goos-H\"{a}nchen shifts [Goos and H\"{a}nchen, Ann. Phys.
436, 333 (1947)] for electron beams tunneling through graphene double barrier
structures. We find that inside the transmission gap for the single barrier,
the shift displays sharp peaks with magnitudes up to the order of electron beam
width and rather small full-widths-at-half-maximum, which may be utilized to
design valley and spin beam splitters with wide tunability and high energy
resolution. We attribute the giant shifts to quasibound states in the
structures. Moreover, an induced energy gap in the dispersion can increase the
tunability and resolution of the splitters.
