Intersecting corners and checkerboards of negative refractive index materials (NRIM) represent highly singular electromagnetic systems that involve very highly enhanced local fields and the local density of modes. It is well known that plasmonic metallic systems can mimic the behavior of NRIM in the near-field limit at optical frequencies. Opaque gold films have been structured by focused ion-beam technologies at submicrometer scales in a checkerboard fashion and their optical properties measured. Subwavelength square holes in thick gold films placed in checkerboard fashion show a broadband extraordinary transmission of light at visible wavelengths. We find that the smaller the square holes, the larger is the transmission over a band of wavelengths from 650 to 950 nm suggesting that such structured surfaces have very unusual effective medium properties, which is confirmed by the band-structure diagrams computed with finite elements. Theoretical results also confirm the experimental transmission measured to be well over 80% from 750 to 950 nm for a checkerboard with 150nm×150 nm square holes. This unusual broadband nature of checkerboard structured films is confirmed by the dark-field reflection spectra. Microscopic studies reveal that these structures have enhanced interaction of light at the edges and corners. These checkerboards are also found to give rise to an enhancement of fluorescence by imbedded dye molecules. There is a strong correspondence between the theoretical predictions and the experimental measurements.