In terms of magnitude of injury, the two fatalities from turning which I've heard about were 1) impact from wood breaking and flying off, 2) long hair getting caught in the turning spindle/chuck. However, the lightenberg burning devices would have to be #1 for fatalities among woodturners.
In a vaguely seriousness order, I would submit:
Chainsaws cause very large, deep, hard to repair wounds. Usually in thighs, but could be feet or lower legs with more serious effects. I've never seen or heard of anyone getting a running chain in the forehead, but I'm sure that has happened to people, and would cause a horrific, likely fatal outcome. Chains flying off the bar can cause facial injuries.
Tablesaws typically shorten fingers, which can be managed but leave the victim with some degree of disability.
Bandsaws could shorten fingers as well, but seem more commonly to make ragged cuts in fingers that head in time.
Routers are amazingly effective at taking clean pieces out of people, occasionally with a little bone. With the migration to router tables, I'm not sure how the injuries have been affected--hopefully they are less.
The typical lathe injuries are well described above. I would add back aches related to leaning over or otherwise being in awkward positions, but that's not very exciting, and they can be reduced by adjusting the height of the lathe and working off the end. Vibration can also cause muscle strain.
No one has mentioned getting things in the eye. Probably we don't consider this an injury and don't identify a little sawdust as a significant problem. However, Metal foreign bodies with speed can be extremely dangerous. This might occur from a saw blade breaking off a tooth or a turning tool hitting metal within the wood. It could also occur from someone striking metal with metal.
Minor cuts are undoubtedly common and not yet mentioned. These would include things like reaching across the sharp edge of a tool, dropping a tool with the sharp edge hitting the foot or shin, having a catch kick the tool back at us, or even getting cut by the sharp edge of a spinning bowl. I bet I go through a bandaid a month but can't recall a single specific injury.
The adverse effects of long term woodworking are well mentioned above, with respiratory being most serious and hearing loss related to chronic noise exposure probably most common. What?