The main advantage of a laptop is that it is small in size and self contained, so it's portability makes it easy to move around. If you are a road warrior then the need is obvious. If you are a gamer you most likely would be better off with a desktop. Most people are between these two extremes, so should evaluate the issues rather than deciding that a sexy looking little laptop is for them!
If you often need to take your computer back and forth to work, on planes or to your second home then the portability is of great benefit. However, this benefit can also be a serious problem in that laptops are stolen at alarming rates. When they steal your computer they will also steal your valuable data.
Should your laptop break, due to their "proprietary" nature, there are a limited number of companies that can fix it, so the repair is often far more expensive than those of desktops. It is amazing how many times I hear about a laptop that has been dropped and the display cracked, resulting in a very expensive repair. I have never heard of that happening to a desktop. People also carry them around open and break the hinge, which is also a very expensive repair.
Laptops are often far more expensive than desktop, $300 to $500 more and often twice as expensive. If you want a really light weight one it might be $1000 more than a desktop. You are paying for the proprietary design and the more compact package, which means more expensive components. Unless the feature of portability is very important it may not be worth the premium. If you are a gamer then there might even be a much larger premium to get a powerful gaming laptop. A large monitor and a very fast graphics board would be a more cost effective investment.
If you spend more than a few hours a day then the small laptop screens, compared to a 17" or larger display you can buy with a desktop would easier on the eyes.
You should also consider the operational cost of owning a laptops. Some people use them for the portability factor and always have them plugged in. Others want to use them on battery power. The batteries often do not last more than 1-2 years. They are expensive to replace at typically $100 or more. If you purchase a brand new laptop they never have more than a one year warranty. Depending upon what you are doing they may not hold a charge for more than an hour or two. So, you need to factor this into your buying decision.
Since, I have been selling laptops for almost nine years it is obvious I am a proponent of laptops. I have one at home and one at work. For doing e-mail or browsing the web a $300 or $400 laptop is a great bargain. However, I firmly believe that like all computing decisions understand your computing needs and then decide whether a desktop or a laptop would be the best choice for your situation.