Every young boy knows the joy of sitting by the campfire and sampling everything he can find to see if it will burn. The answer is yes. But we still try it anyways. Fun, childhood antics aside, what we burn, especially in our home, is extremely important.
Fireplaces are designed to burn firewood. They are not incinerators. A mix of dried hardwoods and softwoods is all that should be used. Although modern fireplaces vent very well to the outside, there is always some exposure to them. Even if the fumes are consumed, burning anything other than wood can add to the harmful pollution outside.
There are several things that should be specifically avoided that some may feel qualifies as firewood. Painted wood should not be burned. Burning the heavy metals commonly found in paint releases toxins that can be harmful even in small amounts. Pressure-treated wood contains arsenic. Even a small section of would has the potential to kill adults. Manmade woods like plywood usually contain formaldehyde.
Enjoy your fire. Just burn wood.