What is the ruling on using images of living beings (such as a bear, cat, child, or woman) as avatars in forums, and what are the consequences of browsing these forums and viewing such images?

There is no harm in browsing forums that contain pictures of animate beings and looking at them, as long as the pictures are not of a woman; due to the Almighty's saying: "Tell the believing men to lower their gaze and guard their private parts. That is purer for them. Indeed, Allah is Acquainted with what they do."