I came across a few bikers down when I was commuting into London last year and they really did make my stomach flip and I felt really bad for them, but once past the scene I tended to carry on riding as normal.
The only one that affected how I was riding was the biker I saw knocked off. It was pretty shocking. 'Filtering' up the inside on commercial road, a jag decides to take a turning on the left to get out of the traffic at the last second, no indicators. I watch as the car clips the aprillia in front of me sending it ricocheting up onto the pavement (luckily there weren't any peds there at the time) and the rider flying through the air.
It was just like when you throw a rag doll. Arms and legs all akimbo and then he hit the deck bounced and spun a bit more before coming to a stop by the curb.
Not entirely sure how I managed to see all that AND execute an emergency stop to avoid plowing into the side of the jag myself, funny how these things work I guess...
Well, that shook me up and I rode like a granny all the way home.