Let me first say that I am not a photographer, it's not a hobby of mine and isn't likely to become one. If I take pictures of stuff it's probably going to be shots of friends and family, or more likely, car parts which I will then post here. I never use a tripod (don't even own one), but do try to brace my hands to eliminate shaking the camera as a cause for blurry pictures.
I had an older FinePix a few years back and replaced it with a Nikon CoolPix 3200. Granted the FinePix was the cheaper model and the Nikon is only the middle of the road model, but I really couldn't be happier with the picture quality of the new one, and the old one was pretty bad. What really used to get me was low light conditions like inside my garage. I'd take pictures and use the flash and they would always come out blurry due to a lack of light. The Nikon has a bunch of different functions on it, but the one that I use most is the flower function, works well for close ups of parts. I guess this is for taking that bee hovering over the flower shot, but it works FAN-friggin-TASTIC in the garage and makes low light photos come out crystal clear. The only complaint I have about the camera at all is that in mpeg mode it has an annoying clicking that seems to be impossible to get rid of, but I didn't buy it for movies anyway.
OLD CAMERA (taken in the daylight with the garage door open, autoflash):
NEW CAMERA (taken in garage with flourescent bulbs, door closed, autoflash):