It depends what you're burning and how you burn it.
If you're burning gas, you're burning it either at the perfect fuel/air ratio or maybe just a little lean. You only get water vapour and carbon dioxide out.
If you're piling up coal in a stove you're getting all sorts of crap out of the chimney, including radioactive dust.
It's one of the reasons that cars have been fitted with catastrophic converters. These remove the CO and HC by reacting it with what little excess oxygen there is in the exhaust stream to turn it into carbon dioxide and water, and at the same time produce massive amounts of nitrogen oxides. It reduces the efficiency by quite a bit but that's okay because it's a tiny effect compared to turning a huge chunk of Africa into a toxic hellscape to mine the palladium and rhodium the catalyst uses.
We'd have incredibly clean cities if we ran vehicles on propane instead of petrol, and in the UK there was a big push to do this about 25-30 years ago. Obviously this got a lot of pushback from the banks and car manufacturers, because it wasn't selling people enough debt. Don't adapt your existing car to run on clean fuel that's mostly burnt as production waste! Sell your dirty polluting petrol car that only gets 38MPG and buy this nice new Cleaner Greener Diesel that gets an incredible 39MPG! And all at only 14.7% APR!
Profit before the environment, as always.