The surface plasmon resonance (SPR) of silver nanoparticles (AgNPs) was studied with the discrete dipole approximation considering different shapes, sizes, dielectric environments, and supraparticles assemblies. In particular, we focused our simulations on AgNPs with sizes below 10 nm, where the correction of silver dielectric constant for intrinsic size effects is necessary. We found that AgNPs shape and assembly can induce distinctive features in the extinction spectra and that SPR is more intense when AgNPs have discoid or flat shapes and are embedded in a dielectric shell with high refractive index. However, the SPR loses much of its distinctive features when size effects and stabilizing molecules induce significant broadening of the extinction bands that is often observed in the case of thiolated AgNPs smaller than about 5 nm. These results are useful indications for in situ characterization and monitoring of AgNPs synthesis and for the engineering of AgNPs with new plasmonic properties.