This is the most popular question that I get on my photography list. The answer, as you might suspect, is "it depends".
Are you happy with your current camera? If yes, then stop here -there's no need to upgrade! But, if there are things about your current setup that annoy you, then you may want to look into purchasing something that suits you better. -Read on!
First, I suggest making a list of things that you need out of a new camera. For example: Faster boot-up time (the time it takes from when you turn the camera on to when you can take the first photo, less shutter delay (the time it takes from when you push the button to when the camera actually takes the photo), or even stuff like a flash hot shoe, the ability to change lenses, an available underwater housing, etc. Whatever you feel your current setup is lacking and you NEED to have in your next camera -write it down!
Second, take a look at where you think this photography hobby of yours is going in the next 3 - 5 years (or however long you'd like to stick with your new camera). If you know you're serious about it and you'd like to become a pro (or achieve professional results), make sure the camera you choose will fit those goals or else you'll end up upgrading again much more quickly than you anticipated, which just wastes money in the long run!
Third, take a look at your budget and try to strike a balance between cost and features. Start looking at cameras in your price range, and actually go to a store and pick them up to make sure they feel good in your hand. People with large or small hands in particular need to do this to make sure that all buttons and dials can be reached easily or else you'll end up frustrated with your purchase down the line. You should eventually be able to use all the camera's features intuitively and without moving your eye from the eyepiece.
After getting an idea of cost, brands, and models, go to the following websites to read reviews so you can be assured you're making a wise investment in your new equipment:
* Steve's Digicams
* DP Review
Optionally, read user reviews as well for more information:
* ...and you can always google the camera brand, model, and the word "review" to get even more feedback on the cameras you are interested in
Once you have gone through all of that, you should be able to make an informed decision. If you choose to buy online, be very careful of some retailers who use deceptive practices like calling you to verify your order, then giving you the hard-sell on warranties and accessories (some of which should already come with your camera!). If you are unsure of the vendor you're thinking of buying from, read reviews for the vendor at VendorsReviewed.com or ResellerRatings.com. Or, do business with vendors who are known to be both fair and have decent prices as well, such as B&H Camera, Adorama or Amazon.
...I'll continue this topic with a post about point and shoots vs DSLR's soon!
If you want further help, feel free to post a comment here or join my Photography_Beginners Yahoogroup and ask for help. It'd be helpful to know what kinds of photography you're into as well as your budget and any specific brands and/or models you're particularly interested in.