Pros

Most AIO are relatively modular in their construction.  They are light weight and simple.   When using a wireless keyboard and mouse with an AIO the only other cord would be the power, which makes moving them easy and portable.  Many also have touchscreens which makes them even easier to use.  Less space is needed.  They are likely not going to sustain any water damage.  Unlike the generic desktops that are out there, AIO have a slicker design to them. They are affordable.

Cons

When you purchase an AIO upgrading them is very limited, basically what you see is what you get.  Because of the design of AIO they hold more heat than a standard desktop.  You cannot run dual monitors on most.  They tend to get bogged down when trying to run cpu intensive software.  If something breaks, you are down until the unit is fixed.

Conclusion

All-in-Ones are basically the same as a laptop, except the screen are typically bigger and less portable. So if you are thinking about purchasing and AIO, maybe take a look at laptops too!  Remember to think about upgrade ability when you are making your purchase, you get what get with an AIO.