I've never caused a crash by blasting through a gap. I have slammed into someone who did the same thing from the other side of the guy beside us (I was on the left, he on the right). I think this was in 2006 or so. He gave me the spot. We talked after the race, he joined my team, so it couldn't have been that bad.
I've fallen plenty of times because someone slid into my wheels, usually in rain or in the last turn or three of a bigger crit (almost always in NJ). I've also fallen over guys who have fallen in front of me, road races more than crits. I got taken out once.
I learned a long time ago (maybe due to other training? because I'm wimpy?) that I have to battle using tactics, not brute strength. Therefore I don't push, I don't jam myself into gaps, I call it if two guys are hesitating (I'll tell them to hold or stay or whatever), etc etc. I can ride such that I can keep other guys from moving me, but in most cases they're trying to move me at a time it doesn't matter so I let them move me, like 5 laps to go or something. 200m to go I won't move.
I'll do field sprints but not the super sketchy ones. Most of the riders I have some inkling what they'll do. The ones I don't know make me think twice. This is true especially when I traveled to races - SoCal, Michigan, PA, DE, and parts of NJ. CT/RI, the regular races I do, I know most of the riders so I have an idea of what to expect.
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"...during the Lance years, being fit became the No. 1 thing. Totally the only thing. It’s a big part of what we do, but fitness is not the only thing. There’s skills, there’s tactics … there’s all kinds of stuff..." Tim Johnson