Mountain bikes are complex machines, and mountain bikers are particular to say the least. Finding the ideal bike setup that works for your body type, riding style, the terrain in your region, and parts that fit your budget can be like shooting in the dark. To add to the matrix of solutions, basically any of the components you change will have an influence on the bike's overall handling. When you do find a piece of the puzzle that fits, whether that's a trustworthy tire or comfy saddle, most riders tend to stick with it. We are creatures of habit and find reasons for all of our kooky preferences.
If you look around at your local trail center next time, you will notice a few common parts on our bikes. Tires like the Maxxis Minion DHF have been established as the unofficial benchmark for a versatile tread, for good reason. In case you missed it, Maxxis just celebrated the 20th anniversary of the Minion DHF, just over a month ago. In an industry criticized for changing "standards" based on fringe engineering work, it would be challenging to find another product that hasn't been changed for two decades (ok, they did make Wide Trail cases to keep up with wider rims). Their ability to work in mud or dust, along with a predictable and consistent turn-in feel, makes them a staple on bikes everywhere.
Another timeless component that comes to mind is Shimano's SPD clipless pedal system. For SPD die-hards, you can see the confusion and resentment in their face when they jump on another bike that doesn't have this system. Their workmanship and mud-shedding capabilities have withstood all riding disciplines for decades too.
29" wheels have definitely found their place in all riding categories, after the frame geometries took some time to catch up. If you're a wagon wheel diehard, could you go back to a smaller wheel size, or would that bike be unrideable to you now?
Maybe that component you couldn't live without is something simple, like a water bottle cage on your bike. Based on the Pinkbike commenters, this is essential and probably near the top of the list for most. I'm still surprised by the demand for this feature. Riders are very opposed to riding with hydration packs that can carry tools and snacks as well.
Something that can't be argued with is the fit and comfort of a seat. Once you find the right saddle, anything else seems like torture. Often you'll see the same tired-looking saddle installed on a brand new bike. Contact points are critical. What about grips? Are you fussed by the plastic under lock-on grips enough that you will go through the hassle to glue and wire simple rubber or silicone grips on for the sake of cushioning?
What is the "must have" on your bike? Are there any other special or quirky parts that you simply cannot ride without?