There seems to be an endless amount of commentary about the differences between raw and JPEG files. If you are so inclined, you can become immersed in debates and conversations that, while entertaining and often times educational, don't provide you with the real world experience needed to gain full comprehension.
The only way to learn (the only way to live) is through action. YOUR action.
If your photography is stuck, it can be tremendously helpful to visit websites and watch videos to help you grasp a better understanding of that which is perplexing you. Here's a video with some real world raw vs JPEG examples.
The above comparison video from Tony Northrop doesn't just explain how JPEGs and raw files differ, Tony shows you how they can and cannot be manipulated in post processing. Which, by the way, is the only reason you would even consider shooting in raw. If you are shooting raw files you either have some serious post processing skills that you want to show off or you have made some big mistakes in-camera that you need to fix. Or, you are taking pictures for a client and rightly need to cover your ass in the event that something unforeseen disturbs the perfection of your photographs. OK, three reasons to shoot in raw...
Raw files cannot even be viewed by most people on the planet. Most people don't have the software needed to see a raw file. But everyone (those with computers or access to computers, at least) can see a JPEG. Eventually, all raw files will be converted to another file type so that the image can be viewed. So, a raw file is only good to the person who will actually be doing the editing of the picture.
Most people are not professional photographers and most people will never need to shoot in raw. Most people edit their photos in free programs like Picasa or with one of Instagram's many predetermined settings. Most people are not nuts for photos but they do like and make full use of their photography in their social media posts.
To be nuts for photos, I mean that you want, no - you must have photos that stand out in every regard. The composition must be well balanced and intuitive to the eyes. Your colors must be dead on. Your exposure has to be right. If you are coo-coo for photos, you need to shoot in raw files so that you can maintain absolute control over your image.
If you are not taking pictures that demand perfection or a lot of attention, your camera's JPEGs will be just fine. If you generally don't want to be bothered, shoot in JPEG as the post processing of JPEG images is extremely simple and absolutely free. JPEGs are as hassle free as you can get.
Above: Raw files are great for photographers that want to or have to pixel pick and pay very close attention to the details in a picture. The raw vs JPEG examples above are HDR images created in Photomatix with the same basic edits applied to each photo. The differences are very small. However, if I wanted to do a lot of editing to this picture, using the raw file will give me a more robust editing platform than the JPEG. If you love editing, shoot in raw. If you don't want to be bothered, shoot in JPEG. Either way, you must get it right in the camera. Raw files offer a lot more latitude but raw files do not give you permission to perform miracles in post production; no matter what software program you use.
But if you are demanding more from your pictures. If you want them to meet exacting standards. If you are a professional photographer and someone is giving you money to take pictures for them, shoot in raw and take the time needed in post to give your client the best that you can offer.
Tony's video above does a great job of giving you some real world raw vs JPEG examples demonstrating how raw files behave differently than JPEG files in post processing. Watch his video to get an idea of what is happening in your camera and to your workflow when you switch between raw and JPEG files.
Then, take you DSLR and put it to the test. Put you, your camera and your editing software to the test to see for yourself.
In the end, there is no right choice. The only bad choice is not to take pictures. For me, I can shoot JPEG and live a very happy life not being bothered by the expensive and overpowered software often needed to create a picture from a raw file. BUT, if you pay me to take pictures for you, I will shoot in raw every time because I do not want an error on my part to hurt you, my paying client.