This thread caught my interest, and while I haven't read all the replies, I still thought I would chime in with some comments... if they have already been mentioned, please forgive my redundancy.
I am going on 59 (this month!) and have been operating chainsaws for about 40 years. I am by no means a professional logger or tree man, but I estimate I have cut and split well over 1000 cords of firewood, and dropped and bucked many trees. I cut my leg once... when I was on a steep embankment and slipped and fell on the bar/chain... luckily saw was off, but slice to leg was still deep and painful.... Lesson 1. you need to be careful around a chainsaw even when it isn't running! Another time I was cutting a downed 18" tree trunk into firewood size pieces... the tree had been dropped on top of some saplings, and as I cut a piece off, a 2" sappling which had been bent under the trunk suddenly was freed and whipped up Knocking my hat off and grazing the front of my forehead with a nice cut... If I had been leaning an inch or two forward there is no doubt I would have had a broken jaw, or worse... Lesson 2. always be aware of stresses that might be working on the piece you are cutting... whip backs, kick backs, etc. can kill you.
In addition to the two issues above, I would add the following:
1. NEVER cut above your head or from a ladder (or bucket!)
2. Always look up in the trees to see dead branches (widow makers), that could break and fall on you as you are cutting
3. Keep your chains sharp!!! Dull chains can cause accidents.
4. NEVER, NEVER, EVER continue to run a chainsaw when you get tired... that is when an accident will happen for sure.