As others have said what are you going to shoot and what is your budget.

If you are are a serious photographer then go for an SLR.

You want a point and shoot camera to replace a 35mm?
Lots of brands out there all mentioned above. All will produce good images.
How big do you intend printing out?
Standard photos, maybe a bit bigger?
If so don't bother going for huge numbers of pixels a 3MP will give good results up to A4 size and will be pretty cheap now.

Make sure it's got a good glass lense and you should be fine.

For ease of use I'd recommend Kodak.

Otherwise go to the shops and try them out. Some new cameras are very small and cute. Good for ladies but if you've got big hairy man fingers a camera with a bigger body might be better.