Integrated all-in-one motherboards are fine for
average applications. In actuality, they tend to be
cheaper, since stuffing more discrete components into a single chip package is making motherboards less expensive to produce.
The big selling point for an all-in-one motherboard is that you don't have to go out and buy additional components. They are inexpensive and very sturdy, in my experience.
The downside to these motherboards is that it performs just adequately. It typically uses older technology or combines resources, such as an AGP video system that "shares" 8 Megs of RAM instead of using a dedicated memory source. The embedded sound systems perform fine, but are far from sonically clean and accurate. If you're building a generic box for your kid or as a second computer, all-in-ones are great. If you have a specific task in mind, such as a gaming computer, opt for externally added components and cards.