A TechLore "Ask the Experts" Question...

Question:

I'm in the market for a digital camera to be used to film my kids playing sports (baseball, soccer, gymnastics, basketball, etc.). I already own a great compact digital camera which is great for stills, but is terrible for taking action shots.

I don't necessarily want to spend a ton ($2,000), but would be willing to spend up to $1,000 or so. What are the best sports cameras out today?