We introduce lossless state detection of trapped neutral atoms based on cavity-enhanced fluorescence. In an experiment with a single 87Rb atom, a hyperfine-state-detection fidelity of 99.4% is achieved in 85 μs. The quantum bit is interrogated many hundreds of times without loss of the atom while a result is obtained in every readout attempt. The fidelity proves robust against atomic frequency shifts induced by the trapping potential. Our scheme does not require strong coupling between the atom and cavity and can be generalized to other systems with an optically accessible quantum bit.