Wear-and-tear can negatively impact accuracy. It usually affects parts that move and are used in the operation of the gun. Parts wearing out usually do not significantly impact accuracy but hurt reliability. Weakened springs in semi-automatic handguns with will start inviting all sorts of feeding, ejection and firing issues. Some springs last for a couple of thousands shots, some for much longer. It is a good idea to have spares if one likes a gun and shoots it a lot. Same goes for other parts that can be easily replaced like extractors and firing pins.
The part of a gun that will give accuracy issues when wearing out is the barrel. This is especially noticeable in rifles. First of all, the accuracy expectations of rifles are higher than for handgun. Any variation will be more likely to be noticed. Secondly, most rifles shoot bottleneck cartridges at a much higher pressure than for most handguns. The heat, pressure and friction upon repeated firing can erode the barrel ahead of the chamber changing the leade dimensions and the bore diameter.
In extreme cases, lands can be ironed out surprisingly far into the barrel. This is especially prevalent with magnum and overbore cartridges that send large amounts of hot burning powder at high pressures along with the bullet. Some barrels in these chambering have a useful life of a few measly hundred shots. This may be plenty in the case of a hunting rifle which does not see a lot of shooting but is significant for long distance rifles that are shot often.
Modern Sporting rifles are also subject to that, owing to the large number of shots people put these guns through. Cheap ammunition with steel core or older surplus corrosive rounds that people tend to turn to for high volume shooting will definitely accentuate the problem. Rebarreling the rifle is the only solution. This is routine work for a gunsmith, and some experienced folks even do it at home (remember: no amount of money is worth your health – leave it to a pro if you can).
High volume pistol shooters can eventually iron out the lands of their barrel. If you are lucky enough that you can shoot that many rounds, you probably will not mind buying a new barrel for the gun (and mount the smoothed-out barrel on the wall as a trophy).
I have known of a first-generation Glock 17 loaner at a shooting range. As a test, the range officer never, ever cleaned or maintained the gun. After a couple of hundred thousands of rounds, the accuracy finally degraded: the polygonal rifling had given the ghost, but the gun still shot and cycled reliably! Not all guns are that understanding and willing to help. Give them some TLC once in a while, and they will return the favor.