Digital cameras forum: easy to shoot/high quality pics--does such a camera exist??

good point

price range $300-$400
smaller camera size
zoom prob not a huge issue
action -- 3 year old and 18 month old -- it's all action

Catching fleeting moments from small children is a challenge, so you need a camera with a short shutter lag.

Here are several choices:

Canon A540 or A570IS
Canon SD600 or SD1000
Casio S770
Fujifilm F30 or F31fd

Here is a link to their specifications:

http://www.dpreview.com/reviews/compare_post.asp?method=sidebyside&cameras=canon_a540%2Ccanon_a570is%2Ccanon_sd600%2Ccanon_sd1000%2Ccasio_exz770%2Cfuji_finepixf31fd&show=all

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This is really a tough one. I have an extremely active 2.5 year old, and so I know how hard it is. All the compact cameras mentioned above will all do quite well when there is enough ambient light (outdoor during day time). But not all will be good enough indoor, and I take a lot of action photos of my 2.5 year old in low light and indoor. One thing I find is that I seldom need to do long zoom for this age, since I prefer to be close to them so that they won't run off or do something hazardous (but you will need longer zoom later when they grow older to participate in field sports). And I prefer not to use flash since this will slow down shot-to-shot time. Tripod is out of the question with a young toddler.
So if you find yourself taking quite a number of indoor or low light photos with the active toddler, then the Fuji cameras may be a better choice (with good high ISO performance). I personally use a D-SLR for my toddler, but this will be a lot over the price range you stated (about 6-10x your expected budget for a good system that performs well in low light without tripods or flash).

If not, just get a film camera and a film scanner or get them processed at a local lab onto CD. Film SLR's are so cheap now that they are even cheaper than entry level digital! The benefit of film is...well its just so easy to use!! A hell of a lot easier that digital, theres 0 menu's just a dial with some different shooting modes, the most complicated part is just loading the film. Plus film is incredibly cheap to process, more so than developing digital, plus you tend to get free film when you process in an hour|! so you dont even have to buy film, making it actually vastly cheaper than digital to share photos with the family.

For very young kids, they don't pose or stop for you. I usually grab the camera whenever I see a potential precious moment, and just use the high speed mode to capture the shots. Usually I'll get a few really perfect ones out of a bunch of okay ones. It is not uncommon for me to take 200 photos in one day and pick a few really memorable ones to keep in the computer, and then discard the rest. Developing hundreds of photos from film is quite an expensive way to pick a few good ones to keep. What I noticed was that in the past, I would wait for the perfect moment before I snap the shot to save films. But I sometimes I missed the moment. Now I just keep snapping like a paparazzi, and then pick the ones I really like and erase the rest from the memory card and the computer. Now I hardly miss any precious moments (a genuine unpretentious smile in its fullest stretch is a fleeting moment that doesn't stop for you to caputre, but if you capture it in time, it is a moment that will touch your heart forever).