The official answer: it is extremely important to warm up before any physical activity, especially gymnastics.
The real answer: it depends on how old you are and what level you're at. If a 20-year-old is working on full-twisting double layouts and he doesn't warm up first, he will very likely get severely injured. If a 9-year-old is working on her cartwheels and doesn't warm up, she'll probably be fine.
As far as what a warm up should consist of, preferences vary HUGELY, but a general rule of thumb is that it should do two things:
1) Loosen up any muscles that may be tight from lack of use within the last hour or two.
2) Get the blood pumping, get the adrenaline up, and get the gymnast ready to go.
GT's right..it all depends on the gymnast and the situation. Warming up doesn't prevent broken bones, it prevents muscle pulls and what not. I personally believe that the minimum warm up should consist of the following:
1. Get the blood pumping--jumping jacks, running, jumping, etc
2. stretch out the legs (straddle sit or stand, go to each side and the middle)
3. splits--if they're able to/old enough--i don't do splits with my preschoolers
4. stretch out the arms/shoulders
5. Roll out ankles and wrists
6. bridge/backbend (ages 5 and up) younger kids I do Table Top (Crab position--teaching them to push down on the floor) Note: some younger ones are able to do bridge