This article from Good Housekeeping gives a great reason to use coffee filters:
4. FAVOR FILTERS
Coffee brewed without a paper filter — in a French press or espresso pot, for example — retains an oily residue that contains cafestol, a substance that raises levels of heart-damaging LDL cholesterol. You could — if you're addicted to your French press — pour your coffee through a paper filter into a cup. Or, just save special brews for an...