Five (carbon dioxide, methane, nitrous oxide, water vapor, and the CFCs ) of the six major greenhouse gases in present atmospheric concentrations do not directly lead to adverse respiratory health effects in humans (ozone, the sixth gas does cause respiratory problems). But reduction in greenhouse gases by reduction in combustion of fossil fuels leads to substantial reductions in emissions of other substances (referred to as co-pollutants) that do cause health effects. Cifuentes et al. (2001) point out that adopting policies to reduce greenhouse gas emissions would have the substantial side-benefits of reducing atmospheric levels of other pollutants that lead to premature deaths, lost work days, unnecessary hospitalizations, additional asthma attacks, and restricted-activity days for people at high risk to elevated levels of air pollution.
Reference
L. Cifuentes, V. H. Borja-Aburo, N. Gouvela, G.Thurston, and D. L. Davis, 2001: Hidden health benefits of greenhouse gas mitigation. Science, 293, 1257-1259.