If folk would like to refute this I suggest instead of looking for examples of limbs falling off trees (yes it happens) but of limbs falling on top of someone sleeping under them. The danger is so slim as not to be worth worrying about, now how do you get to your woodland? that is where you are in danger.
In the last few months I can recall reading two threads over on hammockforums about people losing their lives to falling branchs - one was a young man who IIRC had the tree fall over his hammock, the other was a large limb that fell onto a tent.
I'm sure statistically there are more cars passing on a village highstreet than limbs falling, but what does that really say?
My concern isn't that limbs fall, it is that I could be asleep and unable to react to a limb falling.
Another example: I'd be less concerned to hike through an area where flashfloods occur than to sleep in the same area.
If I were to camp in a Beech forest I would stick to hanging from younger trees.
Also you have to consider the weather too. Just like I'd take more care crossing a street in the centre of a city than a village high street, in high winds I'll pick my camp much more carefully. Remember the gale force winds we had a few weeks ago? I camped out in that and slept like a wain (rocked to sleep in my hammock) but you wouldn't have caught me in a beech wood.
