The thermal conductivity of water- and ethylene glycol-based nanofluids containing alumina $(Al_2O_3)$, zinc oxide (ZnO) and titanium dioxide $(TiO_2)$ nanoparticles is measured by varying the particle diameter and volume fraction. The transient hot-wire method using an anodized tantalum wire for electrical insulation is employed for the measurement. The experimental results show that nanofluids have substantially higher thermal conductivities than those of the base fluid and the ratio of thermal conductivity enhancement increases linearly with the volume fraction. It has been found that the ratio of thermal conductivity enhancement increases with decreasing particle size but no empirical or theoretical correlation can explain the particle-size dependence of the thermal conductivity. This work provides, for the first time to our knowledge, a set of consistent experimental data over a wide range of nanofluid conditions and can therefore serve as a basis for developing theoretical models to predict thermal conduction phenomena in nanofluids.