Currently there are 5 different kinds of Logs in the game, all of which are hollow and a bit rounded with a light wood texture on the inside.
4 kinds of Logs can be found lying on the ground in different biomes, 3 kinds can be created by using a Plow (and this is the only option as of now to obtain Ashenwood Logs), one of these Logs (Mossy Weepwood Logs) will change (into common Weepwood Logs) when being harvested.
All of these Logs can be harvested even without any Power Cells equipped.
Cragwood Logs can be found lying on green grass in Forests and Woodlands, but also under Wildwood-trees in the Jungle, under Elderwood-trees in the Taiga and in the water of lakes or rivers even in Grassland-biomes on the river-bed or ground of lakes often consisting of Mud.
Most Logs can be used as Fuel for Forges; 2 blocks will be needed in this case for each process (of melting or hardening), and they will burn rather slowly, just like common Wood. However Corrupted Wood makes a much more powerful Fuel.
Logs cannot be corrupted currently (as of R26 in December 2015).
Attention: most Logs except for Ashenwood Logs are flammable! So you should be careful when putting torches onto or especially under blocks of Logs (or any other block of Wood or Leaves) in hot environments like Savannahs, Jungles or at Shores. Fire Bombs or liquid Lava will immediately set most Logs on fire.
In hot environments fire is able to spread onto other flammable materials and such a forest fire can burn down a whole forest to nothingness and cannot be extinguished by Water nor other liquids. Fire can stopped from spreading by creating aisles wide enough so flames won't be able to leap over or by claiming the area and disabling the claim option for fire spread. Players who bought the "Pro" update can disable fire spreading for their whole gameworlds.