Air mattresses - convenient, portable comfortable and easy to store away when not being used. But, the mattress is useless until it has sufficient air in it. No one wants to sleep on an under inflated mattress. For anyone who has struggled blowing up an air mattress until you were literally red in the face and out of breath, an air mattress pump is a must have.
Manual air mattress pumps - There are units that you pump using your hands and arms and also models that require you to use your feet and body weight. These are going to be less expensive than electric models and don't support deflating, which is something to consider if you plan to pack the deflated mattress back into a tight storage container. These pumps also work well with low air pressure items, such as basketballs. The hand held models weigh just a couple of pounds, but can require some strength when inflating large items needing high air pressure. An alternative is a floor based pump, which requires you use your feet. Make no mistake, saving money will cost you some physical effort.
Electric air pumps - They run on 110/120 volts AC and plug into any wall outlet. Most come with a nozzle assortment to fit most air beds and other inflatable items. These pumps will inflate mattress, rafts, pool toys and other inflatables very quickly, usually in just a minute or two.
Better quality pumps will also deflate, making the folding and storage of the mattress easier. They'll typically come with multiple nozzle adapters for different size valves, as well as an accordion hose. An extra long hose is a good feature to have when electric outlets are scarce.
An air mattress pump for inflatables like the Coleman air mattress pump should be a high quality piece of equipment.
There are also pumps designed to run off your car's cigarette lighter/accessory socket. Some pumps will run off "C" or "D" cell batteries. Pumps running off batteries will not provide as strong an air flow as will pumps directly connected to a power supply.
It's quite possible to spend as much on a top of the line pump as you spent on your air mattress. These units can come in water resistant plastic enclosures, with the ability to double as a vacuum. In fact, most people buy them for their vacuuming ability, with the inflation capability a lesser concern.
Some manufacturers offer rechargeable air pumps. Plug one of these into an outlet and they will recharge overnight. These typically are mid range products, although they are becoming more and more popular at all price points.
One manufacturer (Aerobed) offers a combination air pump and flashlight in a hand held unit. This is perfect for late night camp setups, and anywhere you go camping where space and weight are concerns. It runs on 8 "C" batteries or a cigarette lighter or car accessory outlet. While the pump functions with both the batteries and DC power, the flashlight only works with batteries. The flashlight also will not function when the pump is in use.