In this paper, we combine experimental dark-field scattering spectroscopy and accurate electrodynamics calculations to investigate the scattering properties of two-dimensional plasmonic lattices based on the concept of aperiodic order. In particular, by discussing visible light scattering from periodic, Fibonacci, Thue-Morse and Rudin-Shapiro lattices fabricated by electron-beam lithography on transparent quartz substrates, we demonstrate that deterministic aperiodic Au nanoparticle arrays give rise to broad plasmonic resonances spanning the entire visible spectrum. In addition, we show that far-field diffractive coupling is responsible for the formation of characteristic photonic-plasmonic scattering modes in aperiodic arrays of metal nanoparticles. Accurate scattering simulations based on the generalized Mie theory approach support our experimental results. The possibility of engineering complex metal nanoparticle arrays with distinctive plasmonic resonances extending across the entire visible spectrum can have a significant impact on the design and fabrication of novel nanodevices based on broadband plasmonic enhancement.