By changing your pickups you can do several things to change or enhance the tone of your instrument. Many times the wood and finish can make the instrument sound harsh or dull from synthetic finishes that are to thick. Changing your pickups can enhance the qualities in your instrument. In guitar production, pickups are basically all made the same and when you put them into an instrument made of different grades of wood material, grain, density, weight and when combined with various necks can make for instruments that can all have a different voice. Players like hotter pickups for guitars or basses that sound harsh with stock pickups. Having a hotter pickup will drive the amplifier easier in some cases and reduce the treble in the pickup depending on the gauge of magnet wire used for the coil and the amount of turns.

Here are some suggestions:

Pickups that are noisy and hum using single coil pickups: There are a variety of pickup models that are humbucking and will help in certain conditions. Try using Stack pickups that have coils stacked on top of each other and the pole pieces are down the center like a single coil pickup. The pole pieces can be rod for a vintage look or bar for a custom look.
Try using a rail type pickup. There are also several makes and models of pickups that can be used with side by side coils for noise free humbucking effect. The rail type pickups can have thin blades like my Hot and Cool Rail pickups or other makes and models that have wider blades like Joe Bardens pickups. There are several models available with adjustable pole pieces and coils that can be wired for custom tone combinations.
You can change your pickups when the pickups are not working properly or need to play a specific style of music.
Pickups are easy to change and most music stores can assist or do the work for you. Some retail stores put the pickups in free when buying an instrument and you want to modify the sound. Check around for stores that offer that service.
Pickups can be changed when you need more output or less output. Many Jazz players like using a clean pickup and one that’s often not over wound will produce cleaner notes. If the pickup is to bright, the tone control can be used to reduce the treble and also putting a small capacitor from the hot side of the jack to ground. By using the capacitor to ground will reduce overall treble in the instrument. I’ve used a .0022 mfd. capacitor that works well to reduce the treble on some instruments.
The majority of pickups are changed because your favorite guitarist is using a similar model in their instrument. My favorite humbucking pickup for the lead position is the JB Model because of the one I made for Jeff Beck in the early ’70s. Jeff is a remarkable guitarist along with Billy Gibbons from ZZ Top that have made so many records with great tone.