If you build your own PC, you can buy the exact components and accessories to tailor the machine to exactly what you want. Actually constructing your own machine *may* save you money which you can put toward other components or keep in your pocket, or invest in your retirement. :)
With an OEM (Original Equipment Manufacturer) PC, you do not have as many choices, although some like Dell have evolved to allow more leeway in specifying your new PC. If you really don't like the idea of plugging the components in yourself, you can come close to building your own with Dell and others who allow you to specify processor, RAM, video/sound and other ingredients.
OEM pc's like Dells but especially HP and Compaqs are not very upgradable and often times include proprietary features. With a computer you build yourself, it is very easy to upgrade since all the parts are part of the ATX standard.
No ... not really. You can't just pick up the phone and call Dell Support and tell them the lights on your DVD drive don't work.
But there are two real positive aspects to this: First, you build it, and you are intimately familiar with how things work now ... and Second, you can get all the help you need right here on the site!
You may very well break a piece of hardware when building your PC, but this is fairly unusual. Most folks realize they're involved in somewhat delicate activity, and behave accordingly. Computer hardware has also become far more stable and less delicate over time. Don't get discouraged if something goes awry - it can happen to anyone, and if you're dealing with a reputable outlet, many times you will be able to replace the component.