"Harmful gasses" and "smoke" are not necessarily the same thing.
Depending on your definition of harmful gasses, burning anything can produce harmful gasses (except maybe hydrogen in pure oxygen - I haven't seen anybody yet calling steam a harmful gas, but things change...). Anything containing carbon produces carbon dioxide when it burns, which due to environmental advocacy, is now widely regarded as a harmful gas due to its greenhouse effects. And air is almost 80% nitrogen, which when heated high enough in the presence of oxygen (about 20% in air) produces various nitrogen oxides which are more directly harmful to human health. This reaction occurs almost anywhere you have a flame, and is a concern in internal combustion engine exhausts. Anything which contains sulfur will give off sulfur oxides, which are even more toxic, and sulfur and nitrogen oxides, in the presence of atmospheric water, are the precursors to acid rain.
As Arkcon says, clean fuels containing only carbon, hydrogen, and oxygen burning completely in well-tuned engines, will produce only carbon dioxide, water, and some nitrogen oxides from the nitrogen in the atmosphere. These leave a smokeless exhaust - smoke is the visible material coming out of a flame, and the gases mentioned above are invisible. You may see some heat haze, but no smoke. If there isn't enough oxygen in the mix, or if there are a lot of double bonds and aromatic compounds in the fuel, you will see grey or black smoke as well, typically deposited as soot - this is due mostly to polyaromatic hydrocarbons, as the molecules in the fuel are reformed during the combustion process and only partially burned. You will also get substantial amounts of carbon monoxide if there isn't enough oxygen to fully burn the fuel. Many polyaromatic hydrocarbons are carcinogenic, and carbon monoxide is of course quite toxic.
In open fires (those which are not part of internal combustion engines), there is nothing to keep the fuel contained near the spark, and you also get outgassing of volatile materials from your fuel. These can include low molecular weight aromatic compounds, esters, and ethers, which are responsible for the smells of incenses and vaporized essential oils, and like every other chemical compound known to man, have some toxicity. (The dose makes the poison). Without containment and forced oxygen or air, there is also more polyaromatic hydrocarbon formation. Wood fires outgas a substantial portion of pinenes and turpentines which can accumulate as tars and resins. Tobacco fires and other cured herbs put out a surprising number of known and suspected carcinogens. And of course, anything burning hot enough is still producing nitrogen oxides.
So the short answer is no, there is nothing you can burn (again, with that limited exception of hydrogen burned in pure oxygen to avoid the nitrogen oxides) that will not put out something that is classified somewhere as a harmful gas.