Camera lighting problem
 

I'm an amateur/rookie when it comes to photography. I've had my 3.2 megapixel FujiFilm Finepix 3800 for about a year now. I'm pertty happy with it, about half the time. It takes excellent pictures when the lighting is ideal (outside and sun shining). Anything less and I have to use the flash. This is understandable and acceptable when indoors, but most pictures I take are outside. I hate using the flash outside, because in my opinion it makes the picture look... not very 'pretty.'

Example:
Perfect lighting- sun shining
http://www.toddfx.com/pics/example1.jpg

Overcast, but still a decent amount of sun - with flash. Not good picture. Very ugly.
http://www.toddfx.com/pics/example2.jpg

Overcast, but still decent amount of sun. No flash. Camera focuses, but becomes blurry from normal hand vibrations. It takes fine if I set the camera on a surface or use a tripod though.
http://www.toddfx.com/pics/example3.jpg

Basically what i'm wondering is what kind of setting, if any, will correct this. I realize the camera can't take a perfect picture 100% of the time, but a lot of the time the lighting seems by far good enough for a picture. In fact I'd think that a flash should never have to be used outdoors during the day. Is this true?
Do all cameras have this same problem, or am I just not picking the right settings? I've tried using the "overcast" setting, but that doesn't do it. I've also messed with the F-stop settings, but theres only 3 to choose from and Auto doesn't work either.
Thanks a lot for your time.

You Basically have a point and shoot camera, with little manual override. There are three things to control light: Film Speed, Shutter Speed and of Course F-Stop. The faster the shutter speed the less light (and loss of Depth of Field)...The wider the lens is openend the more light (and loss of Depth of Field)...The Faster the Film (iso 100 to iso 200 for instance) the less light needs to hit the film to produce an image (However, faster film speed does get grainy). By controlling these three elements one can controll the way a photograph turns out. If I were shooting the squirrels (2nd picture), for instance, I would open up the lens one full (maybe half?) fstop. this would make the squirrels look great. You could also slow down the shutter speed to allow more light (but you might need a tripod to hold the camera steady)...If you are serious get a camera that allows you more controll and experiment.

todd-
if the finepix has shooting modes, try using those like "landscape" or "outdoors"
Also, try setting the ISO to 400, if thats something your camera allows you to do. It might add a little noise into the picture, but as hotdogg mentioned it will give you 1 or 2 stops of latitude

Thanks a lot guys. I'll look into that.