While I don't have a camera that meets your criteria exactly, I can make a recommendation or two. Depending on your needs, I might suggest re-evaluating your need for a >3 MP camera, which brings me to my next point. I have a 2.0 MegaPixel digital camera, with 3x optical zoom. You can view a gallery of my photographs
here. A few select pictures that I'd like to point out are:
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Eagle in flight
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Great sunset
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Friend waterskiing
I believe that for most practical purposes, a 2.0 MegaPixel camera should be acceptable for most average users' needs. If you're a hardcore photographer, I'd recommend going as high as possible (ex: 6 MP, or however high they've gotten now). I would highly recommend optical zoom, an LCD (but I would advise against using it for taking pictures...eats batteries quickly), video capture (not greatest quality, but a nice feature/gimic), rechargable, removable batteries, (I'm not sure for the technical term on this next one) a little light when you push the button halfway down so the camera can focus in low-light situations, manual settings for white balance, shutter speed, etc. if you're a moderately competent photographer (I personally have no use for these things, and simply want a camera that will take pictures when I push the button).
The FujiFilm FinePix 2600 fits the majority of these specifications. It doesn't have sound capture on the video (and has a maximum of 20-second clips, iirc), doesn't have the light thing, doesn't have manual advanced settings, but a few preset options from which you can choose, the batteries are just AA, but NiMH (and/or you can buy your own).