How often do runways need to have typical maintenance?
The pavement requires frequent renewal of the top surface. The frequency depends on the type of pavement and on the weather. Asphalt for instance suffers a lot of damage when it snows and becomes less viscous when it is very hot, causing heavy aircraft to sink.

The main issue with repairing a runway on a major airport like JFK or O'Hare is doing so with little to no impact on traffic. Resurfacing an entire runway can take a long time. Therefore, rather than closing the runway for days at a time, airports try to do as many short maintenance operations as possible at night.
Some operations cannot be done in a single night but can be divided into several perfectly timed tasks, that can be done between 11 PM and 5 AM. Some operations can not be divided into such small tasks and require that the airport closes for a day or more.

The French airport Orly (ORY) for instance has one slab of concrete replaced every night on the runway. This way, the strip can be renewed every other year on average, without disturbing traffic. (I saw a video on this subject once, but can't seem to find it again.)

The results of each runway inspection are compared with the results of the previous runway inspection. Maintenance programs are revised based on the rate of deterioration of the runway. The FAA has various resources to help airport operators plan these maintenance operations. 

But damage done by huge planes is only one of the many things that needs to be taken care of on a regular basis. Moreover, aircraft manufacturers try to design landing gear that reduces the impact of the aircraft on the runway as much as possible (note that airports can charge higher landing fees for aircraft that do more damage to the runway, so airlines want airplanes that don't damage the runway).
The most common maintenance operations are (not in any order, and indicated frequencies are only a rule of thumb, as these will change from one airport to another):


Removing rubber. This is an important one. When taking off or landing, aircraft often skid for a brief moment and leave rubber on the runway. This greatly reduces the adherence of the runway, which has a negative impact on stopping distances. This is usually done with high pressure water.
Cleaning the approach light systems and other visual aids. These get dirty with rubber, tartar, dirt... This operation can be done for instance with a mix of water and sodium bicarbonate, or by using dry ice. 
Checking the quality of the approach light systems and other visual aids. Often, a truck with optometric sensors drives down the runway and measures the luminosity. Sometimes the lights need to be replaced. Airports usually have spares available for every type of light that is used on the runway.
Paint and markings somtimes have to be redone. 
Evaluating the pavement and surveying the structural condition of the runway. Trucks are equipped with all kinds of sensors and go up and down the runway. The measures are used to make a map of the condition of the runway. Sometimes, the runway is divided into sub-sections and a different section will be evaluated every month or every other month, so that each section is inspected twice a year. 
Checking for foreign objects on the runway. On all the airports I visited, this is done by the airport firetruck several times a day. Every few months, they sweep the runway to prevent grass, dirt, pebbles,... from accumulating. 
Repairing cracks and resealing joints on the runway. This is to prevent water infiltrations that have long-term catastrophic consequences. A visual inspection of the runway is performed daily to look for cracks.
Cutting the grass around the runway and on the airfield. The grass has to be kept 2 to 4 inches high around the runway. This reduces the amount of debris that can be blown onto the runway. This also reduces the number of birds and other animals living close to the runway (because nobody wants birds to be ingested by an engine, or a squirrel to be run over). 
Keeping all water evacuation paths clear. No water can be left to build up on the runway, since this would increase stopping distance for aircraft, and may freeze. 


There also are seasonal operations, such as de-icing the runway or removing snow.