Hi Gael,
Welcome to ClubSnap.
First determine what type of camera you want first. (PnS, Prosumer, dSLR).
If you want something small that you can slip in your handbag and carry wherever you go, you may want to consider Sony/Casio for style & compactness. If you are going for good specs, go for the Fuji F31. It may not look as sleek as the Sony/Casio models but it's a pretty little devil. My lady firends usually go for Sony/Casio for their sleek styling and compactness and the cameras have served them well.
For prosumer cameras, you may want to consider Canon S3IS, Nikon Coolpix 8700, Sony R1 or Sony H7/9. You may want to check out the Fuji & Olympus too. Do a comparison between the cameras to see what you need & what you want before deciding which to get.
For dSLRs, do factor in the accessories you need to get and if you are OK with the cost, any model is ok. There is no perfect camera, each user will support the brand they are using but you are the one really using it. So follow your heart and not what others say.
Before you decide which to get, go to a reliable store to get a feel of the cameras to see which suits you and you feel comfortable using.
Enjoy your hunt now and do let us know which you have chosen.