We present a detailed characterization of the recently discovered i-R-Cd (R=Y,Gd-Tm) binary quasicrystals by means of x-ray diffraction, temperature-dependent dc and ac magnetization, temperature-dependent resistance, and temperature-dependent specific heat measurements. Structurally, the broadening of x-ray diffraction peaks found for i-R-Cd is dominated by frozen-in phason strain, which is essentially independent of R. i-Y-Cd is weakly diamagnetic and manifests a temperature-independent susceptibility. i-Gd-Cd can be characterized as a spin glass below 4.6 K via dc magnetization cusp, a third order nonlinear magnetic susceptibility peak, a frequency-dependent freezing temperature, and a broad maximum in the specific heat. i-R-Cd (R=Ho-Tm) is similar to i-Gd-Cd in terms of features observed in thermodynamic measurements. i-Tb-Cd and i-Dy-Cd do not show a clear cusp in their zero-field-cooled dc magnetization data, but instead show a more rounded, broad local maximum. The resistivity for i-R-Cd is of order 300μΩ cm and weakly temperature dependent. The characteristic freezing temperatures for i-R-Cd (R=Gd-Tm) deviate from the de Gennes scaling, in a manner consistent with crystal electric field splitting induced local moment anisotropy.