What is my best option for a digital camera that is not an SLR but can take good action shots?

I honestly don't think you can beat a film slr. You'll save a lot on by buying film and while digital is still catching up. I use a film rebel 2000 but for snapshots I have a digital fugifilm f30. It's a nice camera.

Well,..I have 8 cameras and only 2 are DSLR's(which we use to shoot Football) But some cameras you can check out that have the Lens(power) and High ISO's without too much Grainyness in your Pics would be: Fuji 9000 series(9000,9100 in USA-9500,9600UK/EU) or the new Sony DSC-H9(shipping in a few weeks) The Prices are around the same($500)the differences are The Fuji is a 9Mp, but the Lens is only 10.7X, while the sony is a 15X(they also have a 7.2Mp model with a 12X-the DSC-H5) The Sony uses Memory stick, which i find to be expensive, while the Fuji uses Either xD or Copmpact Flash. While i have used the H5 twice(teaching someone else how to shoot with it) My investment is in xD cards, so i personally use the Fuji, which also has the better battery Life, both with Rechargables and std Alkalines, But.... If your sitting further away, the Sony has the longer lens..... Just stay away from the Panasonics, the bodies are very noisy.

Hmmm... I'm guessing the best action type compact camera you can buy is the Canon S3 IS or perhaps the new Olympus (550 I believe), both are under $500 and may not be too fast. Since you're budgeting a nice amount for your camera why not reconsider an SLR? For about $1,180 you can get a Rebel XTi with a 17-85 (28-135 equivalent) stabilized lens. You don't HAVE to buy additional lenses or filters you know... Ignacio

Whatever you end up with, be sure to try the "Sport" mode, as this will speed up your camera performance considerably. And leave the darn LCD turned OFF to speed it up even more.