Most Logs can be used as Fuel for Forges; 2 blocks of Weepwood Logs will be needed for each process (of melting or hardening), and they will burn rather slowly. Weepwood Logs cannot be corrupted currently (as of R39 in February 2017), however Corrupted Wood makes a much more powerful Fuel.
Most Logs are flammable, so be careful when putting torches onto or especially under blocks of Logs (or any other block of Wood or Leaves) in hot environments like Savannas, Shores or Jungles. Fire is able to spread onto other flammable materials and such a wooden house or whole forest can burn down.
You cannot extinguish such a fire by using Water or other liquids, but only by creating aisles wide enough so flames won't be able to leap over or by claiming the area and disabling the option for fire spread. Players who bought the "Pro" upgrade can also disable the fire spread option for their whole gameworld.