¹H spin-lattice relaxation experiments have been performed for a series of ionic liquids including bis(trifluoromethanesulfonyl)imide anion and cations of a varying alkyl chain length: triethylhexylammonium, triethyloctylammonium, decyltriethylammonium, dodecyltriethylammonium, triethyltetradecylammonium, and hexadecyltriethylammonium. The relaxation studies were carried out in abroad frequency range covering three orders of magnitude, from 10 kHz to 10 MHz, versus temperature. On the basis of a thorough, quantitative analysis of this reach data set, parameters characterizing the relative, cation-cation, translation diffusion (relative diffusion coefficients and translational correlation times), and rotational motion of the cation (rotational correlation times) were determined. Relationships between these quantities and their dependence on the alkyl chain length were discussed in comparison to analogous properties of molecular liquids. It was shown, among other findings, that the ratio between the translational and rotational correlation times is smaller than for molecular liquids and considerably dependent on temperature. Moreover, a comparison of relative and self-diffusion coefficients indicate correlated translational dynamics of the cations.