The National Electrical Code is the authoritative source for electricians, inspectors and builders. Available for sale, the 2011 revision of the code can be found online in small sections, advice forums or summaries. The code does not specify the height of any electrical outlets but has many other things to say about outlet placement.
Because the National Electrical Code is ratified by the states, seek guidance at the state or local level; for most questions, the local level is the best place to start. Each community is different. The City of San Diego, for example, includes moving an electrical outlet in building-code activities that require a permit. Other communities may require a permit and require you to use a licensed electrician or not. If there are height requirements for outlets in the basement or other rooms, this is most likely to be specified by the local building code.
An informal survey of building-advice sites suggests that wall outlets are routinely placed 14 to 18 inches off the floor, barring local requirements, a homeowner's special requests or code issues like electric baseboard heating. If your basement is predictably dry and well above the water table, this may be the best placement for your outlets. Basement outlets are generally required to be placed outside a 6-foot radius of a water source, like a sink. Outlets should be no more than 6 feet apart, and there should be an outlet on any wall 2 feet wide or wider.
Given these varied considerations, it may make sense to put some outlets higher than others. Outlets above a washing machine or dryer and 4 to 5 feet above the floor for tools, treadmills and entertainment systems may make it easier for you to plug and unplug them without reaching behind machinery. High placement also lets you work without tripping over cords on the floor.
The element posing the greatest problem and danger with placement of electrical outlets is water. It is unclear from code summaries whether just one or all the outlets in a basement need to be equipped with ground fault current interrupters (CFCI). Check with your local building department for up-to-date requirements. Give further thought to location of both your circuit panel and secondary power shutoffs so they are easily reached in case of storm damage.