What are the percolation properties of a repulsive point process on an infinite connected graph? To treat this question, one starts by clearly state which definition of repulsivity is adopted here. The first issue is then to identify some repulsive point processes. The most known examples of repulsive point process are determinantal point processes. Are they some others? We construct some examples and give a general answer on their percolation properties. In case of determinantal point processes, we establish stochastic domination relations to obtain other sufficient conditions for percolation.