The worst situation I've been in involved someone getting smashed into a mirror during a fight (inside an unsupervised classroom), and then bleeding profusely.
Yes, I did act. I was almost compelled to act, though honestly I was riddled with adrenaline. I had to actively calm myself down, and I barely managed to do that while considering that someone might actually die. It's hard to think straight during events like those, and I don't blame anyone at all for not knowing what to do.
3 people basically just made a circle and clambered in confusion while one person restrained the guy who flung the other guy into said mirror after throwing some punches.
It even took me a few seconds to consider moving in order to get the staff to respond to me dashing through the hallway, after seeing someone get shards of mirror in their head. Flight or fight...
Also saved someone from cutting off their own hand in a workshop (class effort). Scary as hell, because their sleeve got caught in the machinery and it made this horrible whining sound.
I guess sometimes people play the "It's none of my business, someone else will take care of it" card, until no one does.
tl;dr Yes.
I managed to overcome the surreal flux of adrenaline and basically prevented someone from bleeding out, but it was incredibly hard to keep a leveled head when you consider that someone could die while you're running around aimlessly. I don't blame anyone for standing still and doing nothing, but to be honest I couldn't sit back and watch someone get beat up while 30 people cross the street to catch a bus... even though that someone might actually have stolen a purse.
I'd think it'd be better to find out, while applying common sense (e.g. that guy is wearing a ski mask) instead of leaving it for someone else.
the worst situation that i have witnessed was at my job
a guy basically cut off his thumb and index fingers, since i was there when it happened i had to help slow the bleeding, call 911 and help locate the thumb since the index finger was still attached by a sliver of skin.