Quantum spin liquids (QSLs) are fluidlike states of quantum spins in which the long-range ordered state is destroyed by quantum fluctuations. The ground state of QSLs and their exotic phenomena, which have been extensively discussed for decades, have yet to be identified. We employ thermal-transport measurements on newly discovered QSL candidates κ-(BEDT-TTF)2Cu2(CN)3 and EtMe3Sb[Pd(dmit)2]2, and report that the two organic insulators have different QSLs characterized by different elementary excitations. In κ-(BEDT-TTF)2Cu2(CN)3, heat transport is thermally activated at low temperatures, and this suggests the presence of a spin gap in this QSL. In stark contrast, in EtMe3Sb[Pd(dmit)2]2, a sizable linear temperature dependence of thermal conductivity is clearly resolved in the zero-temperature limit, and shows gapless excitation with a long mean free path (ca. 1000 lattice distances). Such a long mean free path demonstrates a novel feature of QSL as a quantum-condensed state with long-distance coherence.