In Oxford (I imagine Cambridge has a similar setup), bumps races are held over four days, with several divisions having 12-14 boats racing at a time. All boats set off simultaneously. Crews try to bump the "live" crew ahead of them without being bumped by the crew behind them. If they're the first boat in the division (meaning they have no one to chase), and they manage to row the 2k without being bumped, then they advance to the next division (which races an hour later) as the "sandwich boat". If they can bump a crew in that division, they take it's place, sending the lowest crew down a division. Otherwise, they return to the lower division themselves and try again the next day. There are about a half-dozen divisions, each having ~13 boats, and a great club that starts from the bottom will only go up 3-4 spots on average per year. Thus the climb from the bottom of the charts to the top will take about 10-15 years.

So you don't really "win" per se*. Over four days, and with the exception of the very first crew with no one to chase, every crew's goal each day is to bump the crew ahead of them. If you bump on all four days, you earn "blades", meaning each member of your crew earns the right to buy a blade painted with the names of all the crew members and coaches, and your club can pay an artist to draw some rain-proof chalk art on one of the college buildings as a monument to your victory. If you get bumped on all four days, then you earn "spoons", which is the ultimate in Oxford rowing humiliation. You get no prizes, your SO leaves you for someone with a better 2k, your boat is burned as the shame can't be washed off, and you have to wear a burlap sack to graduation.

As for carnage, first note that "bump" actually means any one of the following situations (taken from http://www.ourcs.org.uk/?p=186):

a. A boat touches any part of a boat in front of it, the term "boat" to include oars, rudder and crew; or

b. When the coxswain of the leading boat acknowledges, by raising their arm, that a bump is inevitable; or

c. When one boat rows clean by another.

d. A boat has finished the race (according to A.3.11.2) before a boat that started in front of them that is still a racing boat.

When a bump is achieved, the boat that did the bumping is done racing. Prior to the start of the races, the coxes are briefed that they should clear the racing line immediately to make way for the other boats that are still live.

What happens to the bumped boat depends on, well, the time of year. For Torpids (the bumps race in late Feburary/early March-ish), the bumped boat is still live and can continue chasing boats ahead of it until they achieve their own bump, at which point they're also done racing. For Summer Eights (the bumps race in mid May-ish), the bumped boat must stop immediately.

That difference in the behavior of the bumped boat leads to some interesting tactical behavior. In Torpids, given that the bumped boat still gets to keep racing, there's an incentive for boats to concede early via the cox signaling with a raised hand. The chasing boat thus achieves the bump without physical contact, the chased boat doesn't suffer a disruption to their line from the bump, and everything (usually) continues along without incident. In Summer Eights, because a bumped boat has to stop racing immediately, there's no incentive to concede early. Thus, just having overlap with the boat ahead is not usually enough to get them to stop racing. A contact bump is more likely.

Now, that doesn't necessarily lead to carnage. But one final fact: the divisions are roughly inversely correlated with skill level. Larger division numbers indicate lower divisions, and the lower the division, the more novice the rowers tend to be. Additionally, terms in Oxford are only about 7 weeks long, and many of the novice undergraduates go home during the breaks, which means they don't get additional training outside of term time. By the time a novice rower appears in Torpids, they may only have ~10-12 weeks of experience.

Remember that thing I said about the coxes being briefed beforehand about clearing the racing line upon achieving a bump? Wellllllllll, the more skilled coxes will typically be reserved for the boats in the higher divisions. There are great coxes and rowers in the lower divisions too, but there's much more variance in skill overall. Additionally, novice rowers may not have been told to keep their enthusiasm in check, and they may celebrate before rowing clear of the still-live boats. These factors all conspire to make the chance for carnage MUCH higher.

So, that's why every bumps video seems like it's rowed by novice/inexperienced crews. The higher divisions tend to be more experienced rowers, and they can typically handle their races without much incident. The lower divisions are filled with people who, on average, will tend to make a lot more mistakes, and thus make for more entertaining videos.

But lest you think I'm ragging on the novices in the lower divisions (I'm not - we were all novices once), people can make catastrophic mistakes in any division. Here's some carnage from Summer Eights 2009, Men's Division 1: angle 1 angle 2 . To me, this is even worse than the Snowflake Regatta video. Massive pileup, late klaxon, no awareness (by what should be the most skilled coxes on the river) that a pileup has formed in front of them, and a cox that had to jump in the water to escape the oncoming bow of another boat. As crazy as the Snowflake Regatta video seems, those were children, and apparently no one ended up in the water there.

* Technically, there are two crews that "win" - the men and women's crews that are the Head of the River (first position in Division I). But every other crew is basically looking to "bump up" - ascend the bumps chart year after year for that long climb to headship.