Recommendations for YOU at the VERY bottom with 2 asterisks, but first a whole lot of general info that will help you out before that.
Before I start let me remind you to buy from reputable online dealers such as beachcamera.com, bhphoto, buydig, adorama, ritz camera, J&R, amazon, etc. NOT ebay. There are reputable dealers on ebay, however they also have a lot of “gray market” versions of cameras, that are basically non-US versions. Look around those sites I mentioned to get the best price. Just remember to check resellerratings.com and BBB.org to see the reputation of the vendor. There are a lot of scam artists online these days. I would stick to buying from a site that has positive resellerratings and/or a good standing with BBB.
Another thing to never forget, MEGAPIXELS DON'T MATTER, it's a marketing tool. Any photographer will tell you megapixels have nothing to do with image quality. Unfortunately a lot of people think the more megapixels the better a camera. Megapixels above 5 or 6 are more than enough for most purposes, more than those are helpful when making LARGE prints. Fortunately most cameras these days come with at least 6 so no need to worry about mp. When looking at zoom remember to ONLY LOOK AT THE OPTICAL zoom. Digital zoom means NOTHING. If you want to take another picture immediately after you take one, the prosumer point and shoots and dslrs are better at this than compact cameras (compact point and shoot vs prosumer point and shoot vs dslr explained later). So if you shoot a lot of moving things or sports, you may require a prosumer point and shoot or a dslr. However most compact point and shoots these days can do fairly well on that too, but nowhere near as well as a dslr would. Sure you lose the compactness, but a prosumer point and shoot is a slightly more serious camera, and then of course a dslrs are for strictly serious photographers or enthusiasts.
Here are my general suggestions in each range of cameras, organized by 3 groups, compact point and shoots, prosumer point and shoots (basically higher end and bulkier point and shoots), and dSLRS. These are the 3 different classes of cameras out in the market these days. In general also remember, IT’S THE PHOTOGRAPHER who makes the pictures look good and the PROFESSIONAL who makes the pictures look “professional”. An amateur will get better results with a point and shoot then they will with a dslr. You have to devote time to photography to learn, take classes and understand composition to take better pictures with your cameras. That being said, here are my suggestions for each of the 3 different kinds of cameras in the market.
1) Compact Point and shoots: These are your small credit card sized cameras that most people think of these days when they think of cameras, available at any electronic store pretty much. Very portable and stylish. I would say these are the way to go if you are a casual photographer and just take pictures when you are out with friends, or go for trips, etc. In the compact point and shoot range I would suggest Canon SD 880 IS (comes in gold and sliver). This is one of the best point and shoot cameras out so far and costs around $250 I believe. The other good one, which is like an upgrade of the SD 880 is the canon SD 970 IS. That one costs slightly more. The reason I suggest these two is because canon compact point and shoots are the best there are in that class, and these two stand out from there other models because of their 3 inch lcds and fairly good optical zoom. Since most people who use point and shoot cameras don't use the view finder, these models got rid of that and put a huge and vibrant 3” LCD instead, a smart move. Also they have tons of features that are more than any casual photographer needs. Check them out on the canon website, then buy from reputable dealers.
2) Prosumer point and shoot: These cameras offer a lot more manual control than point and shoots and have higher zooms. They are a bit more advanced than the typical compact point and shoot cameras. They'll also be bulker and more expensive, around $400-600. If you are considering compact and want REALLY good zoom look at some of these prosumer point and shoot cameras, they come with 20x zoom while compact point and shoots usually have 3-5X. If you are considering compact point and shoot and you are slightly more serious about your photography and would like more manual control, I would suggest to consider these as well. In this class of cameras, I suggest Sony HX1 or Canon G10 or Canon SX1 IS. All three of these are excellent, you can compare them yourselves to see which one you like.
3) dslr: These are your really serious cameras, with interchangeable lenses. These will cost a lot! They have interchangeable lenses and offer a lot of flexibility and creative control. When you buy these you buy a system and will build on it with life by purchasing more lenses as you go, flashes, tripods, etc etc. Just one of the lenses alone will cost more than your point and shoot will, so they aren't cheap. Photography is NOT cheap. Don’t only look at the price of the camera body when buying an slr. Dslrs are expensive because you buy a system. Lenses are more important than the body and good glass will run you a lottt more than bodies will. Bodies don't matter, you can always upgrade them but lenses are with you forever. Here are my recommendations for dslrs.
-Entry level: If you’re a beginner, I suggest these and then after you learn everything you can upgrade if you feel it is necessary. I also suggest taking a photography class at a local community college. My suggestions for this range are Nikon D40, Canon Rebel XS (around $500 total or less with kit lens)
-Mid level dslr: Canon XSi or the New T1i ($700 for xsi, $900 for T1i with kit lens). I prefer these to the Nikon ones, however Nikon also has their D60 and their D5000 that you may want to look at.
-More professional models: Nikon D90 or nikon D300 or Canon EOS 40D, Canon EOS 50D ($1000 +). I would suggest these if you have experience in photography or with a film slr or previous dslr. Between canon and Nikon, it’s a personal preference. One is not better than the other.
-Full frame: these are the most expensive cameras in the world and will run around as much as your first car would for the whole system, so I won't recommend these because if you were in the market for these I'm sure you wouldn't have asked any questions here on yahoo answers, you'd be a professional taking photos for a living.
*NOTE: canon and nikon are the two biggest and best companies when it comes to cameras. Canon by far leads the way when it comes to point and shoots. In SLR, it's debatable but I prefer Nikon SLRs and I know many who prefer canon SLRs. Just remember when you buy dslr you get a system that you stick with. Lenses are a lot more important than the body, because body can be upgraded always but lenses stay with you forever. I do highly suggest sticking with Canon or Nikon.
** NOT the sony, too many compatibility issues. Read my guide above regarding megapixels. Buy the canon.