Samsung News Geek

Small, light, very portable and easy to use. Some are simple point-and-shoot cameras, others will have touch screen controls and an integrated zoom lens. Prices can be anywhere between $30 and $600+.
These cameras are great for holiday snaps, family events, or simply to record a memory. While some control can be had over composition etc, compact cameras generally have no manual settings and exposures are completely controlled by the on board sensors.
Some will take standard batteries while others will have a rechargeable Li-ion battery.
Generally there is no room for extras.
If you are not after selling your images but they are more for the family photo albums, then a compact is for you.

The convenience of a compact, but the the power of a DSLR. Fixed lens but usually with a big zoom. Most of the higher end bridge cameras, like the Fujifilm HS10 or 20 have full auto settings plus manual. Some can have extras like a remote release or external flash added. The quality of these cameras is improving all the time. I used to have a DSLR but traded for a bridge. They are light, easy to use and you can get some amazing results with them ( see Craig's Photo Gallery. Many of these pictures were taken with a bridge camera).
A great type of camera if you are just starting out in photography but don't want to spend vast amounts of money. If this is the case, then get one with the manual settings so you can practice using them and see the results.
Image quality on many is now good enough to have salable photos.

For the 'best' photos and getting into photography as a more experienced shooter or even professional. Lots of room for extras. Remote releases, interchangeable lenses, external flash, filters the works.
Some you can get am extra battery grip to increase battery life, power, and ease of use.
Many will still have a full auto setting, but if you are getting into DSLR's then you really don't need to be using it, and will be shooting in more manual settings.
A draw back is more kit to be carrying around, as zoom is dependent on the lens you are using, and it can be awkward in some situations trying to change them to suit you requirements.
This is why I swapped my DSLR gear for a bridge. I found I carry my camera more now, and don't need to worry about dust getting in the camera. For me personally, a bridge is better, and I get results as good as I did with my DSLR.
But if you are going professional then a DSLR it should be.