In zombie dinner parties, it's a bring yourself potluck.
"The normal question, the first question is always; are these cannibals? No, they are not cannibals. Cannibalism in the true sense of the word implies an intraspecies activity. These creatures cannot be considered human. They prey on humans. They do not prey on each other, that's the difference!"
In [REC], all the 'zombies' are controlled by a demon, so it makes them cooperate and even hide. Weapons use was more limited though.
In the Resident Evil movies, the manual states that zombies chew on the living because they hunger for life, rather than flesh. They last for decades before decaying, with food or without.
In the tie-in graphic novels that bridge the gap between 28 Days Later and 28 Weeks Later, it's stated that the Infected don't attack each other because they all give off the same pheromone—i.e., they all smell the same to one another, whereas uninfected smell like ordinary people. One character who figures this out survives by finding a way to negate his natural human scent, and later draws a mob of Infected to attack a rival survivor by lobbing a bomb of perfume on him. Why exactly the pheromone stops the Infected attacking one another is never properly explained, though.
The zombies in Return of the Living Dead exclusively attack the living because they're convinced that eating live brains can ease the pain of being undead.
In The Zombie Survival Guide and World War Z it is mentioned that Solanum causes the flesh of the victim to become highly toxic. Naturally this does not harm other zombies, but may explain the lack of cannibalism if the toxic flesh smells different. In World War Z many people believe they have witnessed zombie-on-zombie attacks; it is revealed that the victims of these attacks were actually "Quislings", people suffering a mental breakdown caused by the Zombie Apocalypse who believe they are zombies themselves... while other people can mistake them for the undead, the real zombies are not fooled.
It's also noted that they don't fight each other because they simply don't perceive anything other than living creatures. A zombie that wants a chunk of human that another zombie wants will keep pulling on it rather than shoving the other zombie away.
Justified in Elantris the flesh of the pseudo-zombie Elantrians tastes so terrible that despite their constant ravenous hunger they can't bear to eat each other.
The zombies in Friday The13th The Jason Strain never attack each other or Jason, the Zombie Progenitor, since they seem incapable of registering a fellow undead entity. The same seems to be true for Jason, who is completely apathetic towards the zombies he is creating, his acknowledgement of them never going beyond shoving some aside when they get in his way.
In Warm Bodies, the Dead must consume living people to take their life force and stay alive, although the implication is that the sparks can actually keep the zombies going just by proximity. They also eat the brains as a sort of high since the brains contain the person's memories, although this is not necessary.
Anime and Manga
Not quite zombies, though most of them use similar tactics, but the Titans in Attack on Titan usually do not eat one another, only humans. But in episode 7 a "rogue" Titan appears that ignores humans and kills other Titans, though doesn't bother to eat them beyond killing one with its teeth, and in episode 8 a bunch of Titans gang up on him and start eating him alive. Then it turns out that the "rogue" was Eren Jaeger, who is apparently a human that can create and control a Titan body, and has a deep-seating loathing of Titans. And even later that there are other Titan-shifters who maintain their intelligence and are leading the dumb Titans to wipe out humanity.
During the "fall" of Wall Rose, there is an odd moment in which one Titan attacks another, pushing it to the ground and ripping its ear off. The victim of this attack then begins eating its assailant's hand. There has yet to be an explanation for this scene, though considering that the Titans in question were the recently transformed citizens of Connie's village, that could have something to do with it.
Strangely enough though, the Marvel Zombies are NOT above fighting each other for the scraps. In fact, pretty much ninety-five percent of the entire horde are destroyed by their leaders (Colonel America and the main five Marvel Zombies present in MZ 2 onwards) when they gain cosmic powers after devouring the Silver Surfer.
The comic version of Hellgate: London had one of the characters belong to the Cabalists, a separate faction of Bad Powers, Good People who use black magic and the demons' powers against their enemies. She uses her arcane powers to coerce a rampaging horde of reanimated undead into believing there was plenty of food among them and devour each other.
In ZA:Zombies Anonymous: zombies who refuse to eat living humans are eaten by the cult of zombies who will.
There are two types of zombies in Silent Night, Zombie Night; the classic shufflers, and a faster and more vicious type that indiscriminately attacks both humans and fellow undead.
Early on in Stephen King's Cell the "zombies" attack each other, but this disappears when they develop a hivemind.
In Mira Grant's NEWSFLESH trilogy, (in "Feed," in particular,) we find that zombies prefer to attack the living, but will attack and consume each other if starving.
Diario de un Zombi has Erico, the lone thinking zombie, explain it's the sensation of life they crave. That said, zombies are dumb as bricks and do eat themselves or others if desperate, confused or angered.
The Wraith of Stargate Atlantis aren't strictly zombies, but they do need to eat humans. One episode did show them as capable of endocannibalism, but since they're intelligent that's probably either taboo or just not a good species-survival strategy (the one who did it was stranded and starving).
The zombies in The Walking Dead hunt by sight and sound, but identify prey by smell. So the movement and sounds made by other zombies will attract them (zombies tend to herd together because of this), but the smell of rotten flesh indicates that other zombies are not desirable as a food source. Two humans were able to walk through a horde of zombies unharmed because they had smeared themselves with zombie guts to make themselves smell rotten - the zombies took notice of them, but did not attack until a rainstorm began to wash the guts (and the rotten smell) away.
In at least one instance, the zombies did eat part of another zombie, who was discovered hanging from a tree by Darryl and Andrea after having committed suicide (or, put more linearly, a man hung himself and his body turned into a zombie but the zombie couldn't get down). However, whether the zombies-eating-his-legs occurred before the zombification or after is not specified.
GURPS: Infinite Worlds has Gotha-zombies, which do eat each other.
The fan-made Zombie: The Coil for the Old World of Darkness has two breeds of zombie: Grandes, which can only eat living flesh, and Jackals, which can eat any decayed flesh. This includes other zombies. The two breeds, of course, do not get along. (Sidenote: this book was created several years before Bleach...)
In the "Shards of Alara" setting, the shard of Grixis is basically a Zombie Apocalypse taken Up to Eleven. There are only a tiny number of human refugees left who use illusion magic to survive, apparently very effectively. The massive hordes of undead are forced to turn on each other - for example, vampires have to try and drink gross, congealed zombie blood. Poor vampires ...
In World of Warcraft, the playable Undead have cannibalism as a racial ability, and it works on both humanoids and other undead.
In Left 4 Dead 2, you can make the zombies fight amongst themselves using boomer bile (they don't eat each other, but they don't eat people to start with, just kill them). You'll occasionally see infighting, and there are some occasions of the mutated zombies fighting each other, like the Tank knocking the Witch dead in order to get to the survivor.
Averted in Warcraft III. Ghouls will eat any killed units to restore health, whether previously alive or undead. Lack of infighting is due to Mind Control.
Zombies are occasionally seen eating other zombies in the Resident Evil series. (Pre-RE4 at least.)
Often averted in Urban Dead: Zombies attacking each other only gain half the XP they get for damaging human players, but it can still be faster than hunting humans at low levels and is even officially endorsed by some hordes. And they can't permanently kill each other anyways. At higher levels the fact that they attack only humans is simply a consequence of the fact that "they know better than to eat each other" is true on a meta level; they're all controlled by real players.
In Plants vs. Zombies, while zombies don't normally go for each other, those that eat a Hypno-shroom will.
In Kingdom of Loathing, the Zombie Master challenge path gets several skills that lets them cannibalise their zombie horde. And any of the "normal" game's zombies will still be trying to eat you.
In Zombie Ranch these twopages explain that the zombies won't eat each other under normal circumstances, but it's standard practice to recycle destroyed or non market-worthy zeds into feed for the rest of the herd.
In Unsounded plods are equal-opportunity-scavengers and will go after anything that moves, be it human, animal, or fellow zombie. (Much to Duane's revulsion.)
In We're Alive the zombies carry away the bodies of their dead. It is later revealed that they keep stockpiles of human flesh for food and may be eating their own dead.