We present the first experimental realization and characterization of two-dimensional skyrmions and half-skyrmions in a spin-2 Bose-Einstein condensate. The continuous rotation of the local spin of the skyrmion through an angle of pi (and half-skyrmion through an angle of pi/2) across the cloud is confirmed by the spatial distribution of the three spin states as parameterized by the bending angle of the ell-vector. The winding number, w = (0, 1, 2), of the skyrmions is confirmed through matter-wave interference.