There are two things you do not want to burn in the fireplace.
Do not burn newspapers, magazines, old bills, or other paper products in your fireplace or stove. Burning paper can produce 1400 degree temperatures in an instant, whereas a normal fire burns at between 400 and 600 degrees. This sudden and excessive heat rise in the chimney causes terminal shock to the chimney liners which are made of clay (similar to a flower pot). The sudden heat can crack these liners in less than a minute! Even replacing one liner can cost $600, with $1200 not being uncommon even for small relining jobs, and the price goes up from there.
Unseasoned wood. The wood you burn should be well seasoned (dry) and preferably hardwood. The wood should be kept dry and well ventilated before use. Wet or green (unseasoned) wood will burn poorly causing a buildup of creosote in the chimney. Do not burn pine, it will coat the chimney with creosote that is difficult to remove, possibly causing a chimney fire.