Laboratory experiments searching for galactic dark matter particles scattering off nuclei have so far not been able to establish a discovery . We use data from the XENON100 experiment to search for dark matter interacting with electrons . With no evidence for a signal above the low background of our experiment , we exclude a variety of representative dark matter models that would induce electronic recoils . For axial-vector couplings to electrons , we exclude cross-sections above 6 \times 10 ^ { -35 } \mathrm { cm ^ { 2 } } for particle masses of m _ { \chi } = 2 \mathrm { GeV / c ^ { 2 } } . Independent of the dark matter halo , we exclude leptophilic models as explanation for the long-standing DAMA/LIBRA signal , such as couplings to electrons through axial-vector interactions at a 4.4 \sigma confidence level , mirror dark matter at 3.6 \sigma , and luminous dark matter at 4.6 \sigma .