The same holds true for milling holders — toolholders for lathes, arbors, chucks, and collets. Keep them clean and check for embedded chips and wear on sliding surfaces. A small amount of grease should be applied to threads and other moving surfaces (except in those rare cases where the tooling manufacturer says not to). As previously mentioned, always use a torque wrench (rather than a well-calibrated arm) to tighten things.
One other thing: Don't ignore the spindle on your machining center or multitasking machine. The taper and the toolholders for that machine should be kept cleaner than your dinner table, and inspected regularly for wear and damage. This is especially true for the "steep taper" machines common in most CNC machines, but the advice applies as well to HSK (Hohl Schaft Kegel) and other not-yet-quite-standard spindles. In either case, a drawbar or spring pack is used to hold the toolholder in place. Check it every month or so with a "force check" device, or you might be unpleasantly surprised one day with a batch of scrap parts.
Finally, take note of the term used in the previous paragraph: "the toolholders for that machine." If possible, it's best if toolholders are assigned to a specific machine tool and kept there. This isn't always feasible, but it does keep the inevitable wear patterns of the spindle and toolholder tapers matched, providing more consistent results than bouncing toolholders all over the shop like a kid without a date at the senior prom.
Whatever the case, remember that toolholder life is finite. Most experts will tell you tooling should be replaced every couple of years, depending on how much action they see (the toolholder, not the experts). They're not just trying to sell more stuff. Metal fatigues over time, causing problems with part accuracy and tool life. If you have toolholders approaching their teens (and in heavy use cases, those just a few years old), it's time to send them to the recycler.