Malthusian predictions--the population bomb, peak resources, etc.--have failed every time someone new puts them forward.
The economics behind it was just wrong. It's somewhat intuitive, which is why it keeps popping back up--that there are finite resources seems to plausibly imply that eventually we run out. But it ignores two key factors: comparative advantage (specialization) and innovation. Comparative advantage observes that more people produces more productive at an *exponential rate (not linear or, as Malthus suggests, logarithmic). Specialization afforded by large populations allows each individual to become far more productive than he/she could be alone. And Malthus (and everyone since) has vastly underrated the rate of innovation that we've been able to accomplish as populations grow (our old friend Nate Meikle has actually been doing pretty cool research on this).