If we're talking about hydrogen fuel cells, although these cars wouldn't emit carbon dioxide, they could release nitrogen dioxide which is toxic. Current carbon fuels you buy from a gas station are usually liquid, but hydrogen seems to be transported as a gas. Therefore it is more expensive to transport fuel cells as it is less dense. It's also expensive to break down other chemicals to obtain the hydrogen.
I think the biggest concern is that hydrogen is very flammable. In the case of an accident, this could be bad...