If the DM Lets Them Stack, They'll Stack
The nightstick (LM 78) (7,500 gp; 5 lbs.) appears simple enough:
Anyone who possesses the rod and is able to turn or rebuke undead gains four more uses of the ability per day.
Probably the assumption was that a creature would wield but a single nightstick and, while wielding it, the creature would have 4 extra uses per day of the creature's ability to turn or rebuke undead.
Things didn't work out that way. The nightstick's problems are legion.
The nightstick is underpriced. The least of the nightstick's problems, the Arms and Equipment Guide—which, while a Dungeons and Dragons, 3rd Edition text, was never updated to 3.5 therefore remaining valid for 3.5 campaigns—says that an item that grants a feat costs 10,000 gp plus another 5,000 gp to 10,000 gp per prerequisite (AE 128). Thus the nightstick should cost, like, at least twice its listed price (see below), granting as it does an ability like the feat Extra Turning (PH 94).
But many items are priced higher or lower than the game recommends, so this isn't really that big of a deal. Further, the nightstick only grants the effects of the feat not the feat feat itself, making the item useless for a creature that, for example, wants to meet another feat's prerequisite using the nightstick.
The nightstick is slotless. It requires only possession not wielding or body slots. This should double its cost, but this also means one can gain benefits from as many nightsticks as one's gp and carrying capacity allows.
The nightstick has unlimited uses. It's limited by the creature who possesses it. Thus infinite creatures all of whom possess the ability to turn or rebuke undead can gain the same nightstick's benefits, albeit not all at the same time.
The nightstick's ability is strangely phrased. It avoids the usual language of modifiers, making unclear whether one can gain the benefits of more than one (or even the same!) nightstick, simultaneously (or subsequently).
These are all likely editorial oversights, but in combination it's why the nightstick quickly became the go-to item for expanding the usefulness of the feat Divine Metamagic (CD 80), in particular in conjunction with the metamagic feat Persistent Spell (CAr 81).
The case for combining the effects of multiple nightsticks
This is the easier case to make. If a creature who can turn or rebuke undead possesses 1 nightstick, he gains 4 more uses per day of the ability turn or rebuke undead. If the same creature has 2 nightsticks, he gains 4 more uses per day of the ability turn or rebuke undead then gains 4 more more uses per day. A hundred nightsticks? The creature enjoys 400 more turn or rebuke undead attempts per day.1,2
It's that simple.
The case against combining the effects of multiple nightsticks
The case against combining effects is far harder to make because of the obviousness of the case for combining effects. Ernir's answer cites the Player's Handbook's glossary's stacking entry, but there's a crucial line that needs inclusion: stacking is defined as
Combine for a cumulative effect. In most cases, modifiers to a given check or roll stack if they come from different sources and have different descriptors (or no descriptors at all), but do not stack if they have the same descriptors or come from the same source
(such as the same spell cast twice in succession). If the modifiers to a particular roll do not stack, only the best bonus or worst penalty applies. Dodge bonuses and circumstance bonus however, do stack with one another unless otherwise specified. Spell effects that do
not stack may overlap, coexist independently, or render one another irrelevant, depending on their exact effects. (PH 313)
It's unfortunate that the Player's Handbook doesn't provide examples of the initial part of that definition and fixates instead almost entirely on numeric modifiers, but using the examples provided later in the definition as guidelines, the more uses from a nightstick would no more combine for an additional effect than would the effects of multiple ioun stones (pearly white spindles) (DMG 260) (20,000 gp; 0 lbs.) or (orange prisms) (DMG 260) (30,000 gp; 0 lbs.), which, while they aren't perfectly analogous (no analogy is), are, I hope, close enough to stave off debate.
That is, for the same reason that a Clr1/Pal4 with Cha 18 can't turn undead 14 times per day, that the feats Font of Inspiration and Psionic Talent provide an increase to their respective points that's linear rather than triangular, and that multiple iterations of resistance to the same energy don't combine to one, giant ability to resist that energy, more than one nightstick in a character's possession can't, according to this argument, grant the character more than 4 turn or rebuke undead attempts per day.3
In fact, because the creature has already benefited from an effect that grants him "4 more uses of the ability" to turn or rebuke undead, the creature can't benefit from any effect that grants him "4 more uses of the ability" to turn or rebuke undead until tomorrow when a new per day begins.
(Even this difficult argument can't address the utility value that comes with a party sharing a lone nightstick, likely an unintended consequence of rapid editing.)
Finally, as jan.supol mentions in this answer, the Main FAQ presents the question-and-answer When a cleric has a temporary bonus to his Charisma score, does it affect his turning check or turning damage? Does it change the number of times he can turn or rebuke per day? (12), with the latter being particularly interesting: The FAQ answers that gaining then losing then gaining again uses per day due to ability score increases aren't considered new uses of the ability when gained the second and successive times.
Thence, if extending this ruling to other areas of the game, the same ruling would apply: gaining extra uses of turn or rebuke undead means gaining the same extra uses of turn or rebuke undead, possibly gaining merely already expended uses. Consider, however, that the FAQ is considered by many an unreliable source.
Bear in mind: I'm presenting an argument here, not making one. It just takes a lot longer to present this one than the other.
"What to do?"
Straight-up banning the nightstick is often better and leads to less animosity than allowing the nightstick yet trying to convince folks of the second argument.
For Further Reading
Wizards of the Coast's site redesign leaves me without a direct link to the Apr. 28, 2008, column of "Ask Wizards" (and that column's absent from the archives), yet that column says that
Q: Can a character benefit from multiple nightsticks (Libris Mortis 78) or multiple orange prism ioun stones (DMG 260)?
A: Neither of these items provides extra bonuses in multiples. The rules for stacking (Rules Compendium 21) do not allow untyped bonuses to stack if they come from the same source. However, this does lead to an interesting question: could a character use a nightstick and then grab a second nightstick to use? The Sage recommends Dungeon Masters limit the nightstick and similar items to one a day.
Also, on discussion forums, this is a hill some folks are willing to die on.
1 That this is reasonable way for a Clr20 to spend his gp shows just how valuable nightsticks actually are to the right creature.
2 As a DM I struggle with this reading because I dislike the nightstick yo-yo: A character capable of making turn or rebuke attempts possesses 1 or more nightsticks. He uses the (4 more × nightsticks possessed) turn or rebuke attempts granted by the nightsticks. He drops the nightsticks, losing possession of them. He picks up the nightsticks, regaining possession of them. He then uses the (4 more × nightsticks possessed) turn or rebuke attempts granted by the same nightsticks again. See, as written, the nightsticks don't even care that its the same character; the nightsticks grant an ability and that ability is lost and regained when the nightsticks are dropped then repossessed. Thus each rod grants unlimited use of (4 more × nightsticks possessed) turn or rebuke attempts for minimal outside-of-combat effort. I cannot believe that was the intent, despite the rules saying that happens.
3 This is the same reason that many prestige classes (e.g. arcane trickster, assassin, blackguard) say at the end of the class feature sneak attack that
If [a class] gets a sneak attack bonus from another source the bonuses on damage stack.
Otherwise, the sneak attack damage would just be the highest sneak attack amount from an individual class. The game considers sneak attack extra damage a bonus even though it technically isn't. (By the way, I've never heard of a DM denying a character his sneak attack
damage bonus if a class didn't have such language, but I'm sure such classes and DMs exist.)