So this is probably the most common thing that people ask for. As for the answer? Well I'm not sure. I guess that there is a simple way to find out and that would be based on type of camera (point-and-shoot, bridge camera or DSLR).
Most of us know what a point-and-shoot camera is and most of us have owned them. I used to have a Casio Exilim which was a great wee thing that went round the world with me and even survived a whole year in Australia. It's about 8 years old now and is currently still going strong in the hands of a relative.
These cameras are now quite decent and there are not much difference between any of them except the usual - price and size. I've also got a Panasonic Lumix DMC-TZ8 which has since been spuerceeded by the TZ10, TZ20 and TZ30. If you've got slightly bigger pockets (both financially and literally) I would suggest the TX30 as it's not too big but a bit chunkier than most of it's relatives however it's got fantastic zoom and takes brilliant shots. A great thing to take on holiday or a night out I think.
I don't really know that much more about point-and-shoots as I didn't get into photography until I got my first DSLR. So if you were interested in taking photos as a hobby and you want something more substantial than a point-and-shoot then you need to have a serious think about what is best for you.
It comes down to bridge vs DSLR at this point. A bridge camera is something that "bridges" the gap between point-and-shoot and DSLR cameras. They don't have interchangeable lenses (although there is now a range called Micro Four/Thirds which do and and an extra dimension this area of photography).
So what's the point of a bridge camera? I suppose it's a decent things to have if you are not really that interested in changing lenses but want something that takes a better shot than your average point-and-shoot. These don't take quite as good pictures as DSLRs but are very versatile and some of them have tremendous zooms or "super-zooms" which are often better than most high end zoom lenses for DSLR. The quality of the picture might not be outstanding but if you were going on a safari, for example, and you didn't know much about photography then something like this would be ideal.
These cameras fall down in two area. Firstly, they are not very good in the dark. They are designed to do so many things that they are not perfect at anything and the lens that is fitted usually has a small maximum aperture e.g f5.6 or f7 which means that the whole the light goes through is quite small. The result of this is that the lens is noyt very "fast" and so is prone to camera shake during low light conditions. Also this has a knock on effect that you often have to use the flash which is usually built-in and so also not particularly good.
This issue with the small aperture also leads to another issue with these cameras. One of the most pleasing parts of a professional photograph is the "background blur". This is created by the light bending onto the sensor and really is only influenced by the aperture. The bigger the aperture (counter-intuitively, the lower f-number) the more blur is created. There is a post about depth-of-field (DOF) earlier in the blog which you can read to get you up to speed on this.
Consequently, these bridge cameras don't have as good a background blur as the DSLRs do. So if you are after something a bit more versatile and you think that you might be pursuing photography as a bit more than an occasional hobby then perhaps DSLR is what you should be looking at.
There are loads of these to choose from and it can be a bit of a minefield. I think the most useful thing I could tell you would be to take a look at either Canon or Nikon (sorry to all the Pentax / Sony users out there). Simply speaking these two are the biggest producers of DSLRs and their appropriate lenses so you have more options available with these two companies.
Entry level wise, there are plenty of options and I would suggest picking what you can afford and then going to Jessops and putting them in your hand and seeing which feels right. The body is not that important to begin with and in fact the lenses are more important. Most come with a 18-55mm kit lens and these are crap. If you can stretch to it then get something with a bit more versatility like 18-105mm and also get yourself a 50mm f1.8 which is the cheapest but one of the best lenses on the market. This will take brilliant portraits regardless of the camera body you are using.
I would also suggest that once you have found the camera body for you then try to stretch to the one above that. It's not that big a deal but for a little bit more money you might get something that's a bit more durable, has a few more features and it probably going to last you a bit longer before you have to upgrade to some else.
That's just a few thoughts that might help you decide. If you want my honest opinion as to what you should buy then get this...
Hope that's of use.