Photos for screen saver? Check
Photos for printing 5×7? Check
Photos for Printing 20×30? Most don't really do this as its expensive.
This will determine what camera you want.
Frankly speaking, if you stitch pictures together then an old 3MP camaera is perfectly acceptable for all of the above. I have them hanging on my wall to prove it. If you pixel peep yes, you can tell, otherwise from more than 3 feet away you cannot. For the first two of the above an old 3MP camera is perfectly acceptable for prints up to 11×13 all day long. For cropping purposes, a 6mp cameras helps. After this, the only thing you really want is image stabilization.
What helps even more is the lense. Get a fast lense. F2.0 is good. Most compacts aren't this fast. A very few select compact cameras have this. Start there then look at zoom range. Two such cameras are listed above in previous posts. Get their older cousins and save yourself $200 from the latest and greatest cameras whom are no better than their older siblings.
BUT!
BUT! Cameras with larger sensors have far better color profiles used in them creating far smoother realistic images.
Optimum for me personally is the GH1 and GH2 put out by panasonic. I have not personally used the GF1 or Olympus PEN cameras. Of course they cost a lot more. But, you get what you pay for as well. Everyone and their mother, sister, and brother wants a Panasonic GH2 and Panasonic currently can't build them fast enough. Gives 1080p 24fps video good enough to shoot a real movie. Total weight with a 3x zoom is about 1.2lbs. Extra battery needed though as their batteries are rather small though I have gotten 600 pics without flash on them. Also, every Micro four thirds camera without a mirror can put Every lense ever made on them. = ability to buy very good cheap lenses.
Nikon d7000 would be my next best favorite as Nikon has the best color profiles IMO. Of course here we are talking 3lbs of gear. 2lbs for the camera and a minimum of 1lb for the lense. More like 2lbs for the lense when all is said and done for around 4lbs of gear total. Of course in this range there are a myriad of options ranging in price from $300 on ebay to $1500 etc.