Overexploitation of renewable resources today has a high cost on the welfare of future generations. Unlike in other public goods games, however, future generations cannot reciprocate actions made today. What mechanisms can maintain cooperation with the future? To answer this question, we devise a new experimental paradigm, the 'Intergenerational Goods Game'. A line-up of successive groups (generations) can each either extract a resource to exhaustion or leave something for the next group. Exhausting the resource maximizes the payoff for the present generation, but leaves all future generations empty-handed. Here we show that the resource is almost always destroyed if extraction decisions are made individually. This failure to cooperate with the future is driven primarily by a minority of individuals who extract far more than what is sustainable. In contrast, when extractions are democratically decided by vote, the resource is consistently sustained. Voting is effective for two reasons. First, it allows a majority of cooperators to restrain defectors. Second, it reassures conditional cooperators that their efforts are not futile. Voting, however, only promotes sustainability if it is binding for all involved. Our results have implications for policy interventions designed to sustain intergenerational public goods.