Pickup Truck
A good place to start is with a basic pickup truck. Begin with a regular car base, and add a larger set of wheels. Car bases come in some sets, but are usually about four studs wide. Build the bed on the back and the cab on the front. Use bricks that match the color of the vehicle you want to build.
Tow Truck
Tow trucks bear a striking resemblance to your average pickup truck. So, building one is as simple as taking a similar design to the pickup, reinforcing the bed and adding the tow rig. In reality, tow trucks are wider than most cars, so bumping the bed up to about six studs in width would not be unusual.
Sixteen Wheeler
Sometimes called semis, these massive road haulers should come in a couple of parts. The rig itself is the cabin and drive train. A design similar to a Police Truck might be a good way to start building the cabin. After that, building a trailer is the challenge. These usually run two to three times the length of the cab and are large and hollow, with a connector point to attach it to the rear of the truck rig itself.
Fire Truck
These vehicles are usually considerably larger than your average road vehicle, almost the same length as a semi's trailer and about as wide. Start with a longer wheelbase, and build up walls using red or yellow bricks. Having a ladder on the top or hoses on the sides, as well as room to fit several LEGO firefighters, is a nice customization.
Dump Truck
Beginning with something like a semi truck cab, you could easily attach a dump bed by extending the rear and adding a tilting mechanism. There are a number of options for this, even some pieces with sturdy hinges, to which you can attach the large dump bed. An eight-by-six-stud bed with two or three rows of bricks is a solid beginning.
Miscellaneous
A police prisoner transport or series of construction vehicles aren't specifically trucks, but they are similar enough to be an interesting project. A prisoner transport would be much like a fire truck, only the rear section would be dedicated to a portable prison cell, instead of firefighting equipment; where the ladder or hoses may have gone, place a rear door. Construction vehicles, such as a bulldozer or a backhoe, might also be carried to a construction site on a flatbed trailer.