The wavelength corresponding to the extinction maximum, lambda (max), of the localized surface plasmon resonance (LSPR) of silver nanoparticle arrays fabricated by nanosphere lithography (NSL) can be systematically tuned from -300 nm to 6000 nm. Such spectral manipulation was achieved by using (1) precise lithographic control of nanoparticle size, height, and shape, and (2) dielectric encapsulation of the nanoparticles in SiOx. These results demonstrate an unprecedented level of wavelength agility in nanoparticle optical response throughout the visible, near-infrared, and mid-infrared regions of the electromagnetic spectrum. It will also be shown that this level of wavelength tunability is accompanied with the preservation of narrow LSPR bandwidths (fwhm), Gamma. Additionally, two other surprising LSPR optical properties were discovered: (1) the extinction maximum shifts by 2-6 nm per 1 nm variation in nanoparticle width or height, and (2) the LSPR oscillator strength is equivalent to that of atomic silver in gas or liquid phases. Furthermore, it will be shown that encapsulation of the nanoparticles in thin films of SiOx causes the LSPR lambda (max) to red shift by 4 nm per nm of SiOx film thickness. The size, shape, and dielectric-dependent nanoparticle optical properties reported here are likely to have significant impact in several applications including but not limited to the following: surface-enhanced spectroscopy, single-molecule spectroscopy, near-field optical microscopy, nanoscopic object manipulation, chemical/biological sensing, information processing, data storage, and energy transport in integrated optical devices.