We present high precision measurements of the penetration depth \lambda of single crystals of \kappa-(ET)_2Cu[N(CN)2]Br and \kappa-(ET)_2Cu(NCS)_2 at temperature down to 0.4 K. We find that, at low temperatures, the in-plane penetration depth varies as a fractional power law, \lambda\sim T^1.5. W hilst this may be taken as evidence for novel bose excitation processes, we show that the data are also consistent with a quasi-linear variation of the superfluid density, as is expected for a d-wave superconductor with impurities. Our data for the interplane penetration depth show similar features and give a direct measurement of the absolute value, \lambda(0)=100\pm 20 \mu m.