We report the properties of plasmons in dense planar arrays of silver single and double nanostructures with various geometries fabricated by electron beam lithography (EBL) as a function of their size and spacing. We demonstrate a strong plasmon coupling mechanism due to near-field dipolar interactions between adjacent nanostructures, which produces a major red shift of the localized surface plasmon resonance (LSPR) in silver nanoparticles and leads to strong maximum electric field enhancements in a broad spectral range. The extinction spectra and maximum electric field enhancements are theoretically modeled by using the finite element method. Our modeling revealed that strong averaged electric field enhancements of up to 60 in visible range and up to 40 in mid-infrared result from hybridization of multipolar resonances in such dense nanostructures; these are important for applications in surface enhanced spectroscopies.