We derive structural parameters for similar to 2000 globular clusters in the giant Virgo elliptical Messier 87 (M87) using extremely deep Hubble Space Telescope images in F606W (V) and F814W (I) taken with the ACS/WFC. The cluster scale sizes (half-light radii rh) and ellipticities are determined from point-spread-function -convolved King-model profile fitting. We find that the rh distribution closely resembles the inner Milky Way clusters, peaking at r(h) similar or equal to 2.5 pc and with virtually no clusters more compact than r(h) similar or equal to 1 pc. The metal-poor clusters have on average an r(h) 24% larger than the metal-rich ones. The cluster scale size shows a gradual and noticeable increase with galactocentric distance. Clusters are very slightly larger in the bluer waveband V, a possible hint that we may be beginning to see the effects of mass segregation within the clusters. We also derived a color magnitude diagram for the M87 globular cluster system which shows a striking bimodal distribution.