There are a few parts to the control system for an aileron in a light aircraft, such as the rods, bellcrank, cables, chains etc. What are the main reasons for aileron failures and what parts wear the most during their time?
When talking about that sort of thing, you're really looking for single-point-of-failure weak links that are difficult to detect during a walkaround or inspection. Hinges don't normally just let go with no warning. They get loose and sloppy first. Same with bellcrank bearings, rod ends, and pulley bearings. Things in general on airplanes can get really loose and sloppy and still work because there are large fudge factor margins built into the design (like, a crack on a piano hinge might have to progress to 80% across it before normal loads would make it break).
If you're talking about "aileron failure" as in "spontaneous complete loss of aileron control", this is an extremely rare event. If you had to pick something, you'd generally look for items that can just degrade with no obvious signs and then suddenly let go. On the typical single-loop cable run control system you'll find in a Cessna or similar, that weak link is the control cable itself, at swages and where the cable bends to go around pulleys, or from corrosion. The check for cable degradation, besides visual inspection, is to wrap a rag around the cable and pull it along feeling for wire snags (or you can use your bare hands if you enjoy the potential for surprise searing pain).
For cable corrosion, it can seem attractive to go with stainless cable, but stainless cable is weaker and SS doesn't like to rub against itself and the cable tends to fret and break down at pulley bends (why aircraft SS cable has a lubricant in it - the identical-looking SS cable you get at the hardware store doesn't). In the transport world and in GA I think, you will find mostly galvanized carbon steel cable, which is stronger and doesn't break down as readily (the zinc is a very effective inter-strand lubricant, as well as corrosion preventative).
In terms of overall wear and tear, generally it's parts with moving bearing surfaces that see concentrated loads. The aileron hinge closest to the control rod will always get loose and sloppy first. The bearings in the bellcrank in front of the aileron where the bearings are under a constant radial pre-load from cable tension, on top of flight loads. Pulley bearings at 90 degree bends where radial loads are high. Pulleys and bearings oriented horizontally go bad sooner than vertical ones because the oil component of the grease in the bearing leaks out over time and the bearing rots out.
In the end though, most of the degradation isn't wear and tear, it's degradation from lack of use. Like cars, airplanes do not do well sitting stationary for long periods, especially outside.
Flutter due to excess airspeed is one of the more common failure modes for ailerons that operate via a mechanical linkage. In some cases even adding an extra coat of paint or gel coat to the ailerons without careful rebalancing can promote flutter at lower-than-expected airspeeds. (See service bulletin or Airworthiness Directive on Libelle sailplanes.)
This answer assumes that problems that develop gradually over time and can be detected by normal preflight inspections plus regular annual inspections are outside the intended scope of the question. There are undoubtedly many other reasons besides flutter why ailerons and their associated linkages sometimes need maintenance.
I heard of one a long time ago - I think in Undergraduate Pilot Training. Seems an F-86 was undergoing IRAN, (Inspect and Repair as Necessary), sometime in the 50s, and the mechanic working on the aircraft was an older guy with many years of experience working on other types, but new to the F-86. The F-86 ailerons apparently had a space problem in the bottom of the hinge area that required the bolt that attached the control surface to the hinge to be inserted from the bottom, in order to prevent the lock nut that was on the other end of the bolt from binding. This mechanic, in his infinite wisdom, decided that inserting a critical bolt from the bottom, where it could just fall out if the bolt ever came loose, was a bad idea, so he reversed it and inserted it from the top, and put the lock nut on the bottom. The next time the aircraft flew, when the pilot attempted to roll the aircraft to turn out of traffic, the aileron jammed and the aircraft (and pilot) were both lost.
As I was told the story, apparently, the accident investigation officials, after determining the cause, elected to not inform the mechanic of what he had done, but simply had him reassigned to an area where he could not repeat his mistake. Don't know if this is true...