Cost
There is a wide variety of component options available for desktops, allowing for a large range of prices, but the starting point is relatively cheap. Desktops can start as low as $400 for a full package (computer & monitor) and still be a pretty powerful system. Laptops can have a fairly wide variety of component options, but they are more limited than desktops. To get a more powerful laptop (higher speed, better graphics, more storage space, etc.), the price can be considerably higher, ranging up to $1500 or more, depending on the brand.
Portability
Desktops are large in size and have a separate monitor. While it's possible to take a desktop from place to place, it's cumbersome and not the choice for portability. They are designed to be used in a single location and not moved around much, if at all. Laptops are very portable due to their compact size. They were designed to be taken from place to place, carried in a backpack or laptop carrying case. They are great for on-the-go use.
Processor
Desktop processors are a little bit larger in size, but this also means the desktop processors can be more powerful than laptop processors. New, advanced processors on the market are typically available in desktop computers first. Laptop processors have nearly caught up to desktop processors, but are still limited when compared to desktop processors. Gaming laptops can have an equal performance, but have a much higher price.
Ease of assembly
Setting up a desktop takes a bit of extra work to hook everything up, start it up, and begin to use. It also requires more space to set up. While it's not difficult to connect everything together, it is still more cumbersome than a laptop. Laptops are built to be easy to use, requiring little time to get running. Take it out of the box, plug it in and press the power button. Within minutes, the laptop is ready to use.
Keyboard
Desktops can make use of full size keyboards, including a number pad. There are really no limitations. Smaller laptops with the 14" and 15" screens typically have smaller keyboards and don't feature a number pad on the right side. Larger laptops with 17" screens do have larger keyboards and may include a number pad, but the laptops are bulkier and heavier.
Screen size
Desktop monitors can be 15" or larger. It is even possible to hook up a desktop to a TV, so screen sizes could be as large as a TV. This provides for great flexibility on what the desktop is used for and in what environment. Since portability is a big feature of laptops, smaller screen sizes are necessary and screen sizes typically range from 10" to 17". However, a laptop can still be connected to an external display and support any size of monitor, screen, or projector.
Upgrading
Most components in a desktop are easily removable, making it easier to upgrade and since desktop cases are usually much bigger they're easier to work in when doing any upgrading. Memory and hard drive are about the only components that can be upgraded in a laptop. The remaining components are either built-in and not removable or the laptop is not designed to work with an upgraded version of a component. A need to upgrade anything other than the hard drive and memory usually requires a new laptop.
Gaming
Desktops are capable of using high-powered video cards that have higher power requirements and require better heat reduction/dissipation. Due to the space in a desktop and the capability of using 1000+ Watt power supplies, virtually any video card could be used in a desktop, including two or more video cards at the same time. Physical space is limited in a laptop, which can limit the graphics capabilities. While higher-end laptops can provide better than average graphics for gaming and CAD-based applications, the heat reduction/dissipation is limited by the space in the laptop case. Power is also limited which doesn't allow for video cards needing those higher amounts of wattage to run.
Repair
Repairing a desktop computer is much easier since most of the hardware can be easily purchased off the shelf of any local computer retail store. For most users opening a laptop to repair a part can be difficult and finding a replacement part often requires calling the computer manufacturer or ordering from another online site.