Jumanji/WMG

The game is alive and it wants to be played.
Over and over again... The game senses potential players, and lures them with drum sounds only they can hear. Taking out the pieces 'starts' a game automatically. An accidental drop of the dice 'makes' a move. The game demands on being played fairly too - Van Pelt won't kill the innocent, even those who are players, and the game doesn't appreciate being cheated on.

The game itself is the player.
The game plays against the human players under the pretence of a board game for up to four. The game takes a 'turn' in the form of releasing incredibly dangerous jungle things. The game wins if it manages to kill the human players, or if it takes over the environment and turns it into a real jungle. Every time the game is disposed of, it uses it's drums to lure in new players.

Jumanji and Zathura are Shadow Games based on non-Egyptian magic.
Presumably, these types of Shadow Games work on different rules, which is why the players don't have to be in the presence of their challenger.

Jumanji was created by natives of the jungle to train youth into brave warriors and hunters.

 * Maybe it was a type of Training from Hell for most tribes who had to go under a brave ritual to survive the horrors of the game. Whoever had mastered the game's challenges was declared the winner and the game resets, ready for new hunters to prove their might

The games run off magical virtual reality; they don't change real reality.
Zathura and Jumanji unleash their horrors, not by unleashing animals from another words, but by inducing the players into a magical Matrix VR. All the players involved experience the same hyper-realistic Matrix. The game can predict the future, and so can depict the Alternate Future of what would happen if the game was played, but left unfinished (such as that guy getting fired and people freaking out over Alan's mysterious disappearance).

Evidence for this theory: the complete Reset Button when the game ends. It would create a major Temporal Paradox if everything in the game was real; but a magical Matrix can handle it fine.
 * This troper can't think of a single thing about the reset that would cause a Temporal Paradox.

Van Pelt is always modelled on the father of the player who gets sucked into the game or rolls the dice to summon him from the board.

 * "A hunter from the darkest wild makes you feel just like a child." The rhyme and Van Pelt's appearance (played by the same actor as Alan Parish's father) seem to bear out this theory. If any of the other players had rolled the dice to summon him, he would have looked like their father instead.
 * Or maybe anyone that caused stress in the player's life (as this could be verified).

Van Pelt is a previous player from a session that never ended for him
Just like how Alan got sucked in. But Van Pelt had different rules for getting out. Alan had only to wait for a five or an eight; Van Pelt is trapped until somebody else rolls the "sucked into Jumanji world" scenario, and then he must kill that person. That's why Alan was so terrified of him; they clearly met in Jumanji world, and Van Pelt wanted to kill him. That's also why, the very next time Alan rolled, it brought Van Pelt into the real world. As the only two people who've been inside Jumanji world, their destinies are intertwined. That's also why Van Pelt only wants to kill Alan, and has no desire to kill anybody else.
 * A good theory, but where was his playing piece? Sarah and Alan's pieces where stuck in their places when Judy and Peter began playing.
 * You're assuming there is only one Jumanji Board. We're only shown one—there could be quite a few.
 * But didn't he mention that he tried to kill whoever rolled the dice?
 * Or perhaps he also had to wait for a 5 or an 8, like Alan, but his game ended without either number showing. No, wait, never mind. This theory is fatally flawed. (Exactly what the fatal flaw is will be left to the other Wild Mass Guessers, but it probably involves ancient unfinished Jumanji games.)
 * Actually, this may work if you combine it with the WMG below: Van Pelt gets sucked in but nobody else from his party rolls the needed dice afterwards. To make it worse, the entire group was killed over the course of the game. With no logical way to finish the whole game, Jumanji resets itself, trapping Hunter Van Pelt into it.

Expanding on this:

Van Pelt is a player from a previous game who became trapped and went native.
Van Pelt was a big game hunter in our world during the early-to-mid 1800s (judging by his clothing and rifle) who discovered the game lurking in the African jungle. Though the porters tried to warn him and the rest of his hunting party that it was bad mojo, he sat down for a nice board game one evening with his buddies. During the course of the usual proceedings, nearly the entire group was killed by the jungle hazards. Van Pelt, now quite insane and frustrated that this was something he couldn't kill, asked the spirit within the game to stop playing around and fight him properly. Its answer was to the effect of, "Okay, fine," and so it sucked him into its jungle. Unlike Alan, who constantly sought a way out of the game, Van Pelt decided he was thoroughly enjoying this new challenge and gave himself over to the game entirely.
 * Given his immaculately clean appearance (pre-paint can collapse), his lifestyle inside the game would probably be similar to what he was familiar with beforehand. This would make him even more of a Jerkass, or even a Complete Monster, for hunting poor Alan rather than taking him in.

Van Pelt and Alan are related.
We know that the last people who had the game were also from around there, and Parrishes have clearly been a prominent family in those parts for a very long time. While first looking around the house after moving in, Peter finds a bust of some guy with sideburns just like Van Pelt's (maybe it was actually him). He isn't just played by the same actor as Alan's father for the heck of it; it's to show the family resemblance. As already noted, he apparently got himself stuck as a permanent part of the game long ago.

If a game has only one surviving player, then that player is added to the game.
A variant on the "Van Pelt gone native" theory above.

This has two purposes: it prevents people from abandoning games because they think their victory is trivial; and it punishes players who won't cooperate with the other players.

Alan Parrish and Sy Parrish from One Hour Photo are the same person.
In 1995, as Jumanji ends, Alan Parrish is about 38 and appears to have the perfect life. Clearly, something terrible and life-shattering happens in the seven years before the events of One Hour Photo take place. He changes his name and moves to Los Angeles, alone.

His disturbed personality traits during OHP make sense. Alan's relationship with his father has severe problems which are resolved only superficially; and nobody could possibly spend twenty-six years, including most of their later childhood, in a terrifying, hostile environment all alone and come out as okay as Alan appeared when Jumanji ended.
 * NOOOOOOOOOOOOO! My childhood!

Van Pelt's reason for trying to kill Alan was...

 * To stop the game from continuing and leaking more destruction into the real world. He was merely stalking Alan in the jungle in an attempt to travel with him and kill the players before they could bring more horrors through and endanger their society.


 * To go back to the real world in Alan's place. After all those thirty-odd years of trying, things got personal, so when he became one of the game's perils, he decided he would rather sew his loose ends than try to explore the real world.


 * He never wanted to kill Alan. The game created him to help Alan face the fear of his father, and if he actually had stood up against Van Pelt, Van Pelt would have disappeared. His shots were intentional misses (except the one he knew Alan would foil by declaring Jumanji), but Jumanji made him too good, so everyone that got in his way was in real danger of being killed.


 * Alan rolled the dice that summoned him. It's just what he does.

The board game is an Eldritch Abomination that turns universes into copies of itself when the game is lost.
If someone lost a game of Jumanji, everything would come loose and spread and spread until the real world was a jungle world like Jumanji. It would then go around looking for more universes to convert.

Jumanji's a curse from vengeful jungle spirits.
They're angry at 19th century safari dudes for ruining their unspoiled nature, so this is the punishment. It comes in the form of the kind of amusement westerners enjoy, and hits them with perils based on the Darkest Africa stereotype. Definite ironic punishment. If there's an Egyptian version to punish graverobbers, it definitely has stiff-armed living mummies and other crap they were afraid of. Zathura, by extension, is a pre-emptive one for spoiling outer space.

Everyone survived in the 1995 timeline.
Alan and Sarah, and the poison in  's system gets. Granted, it's still kind of depressing for Alan, who believes he and his father never had the chance to reconcile in any way, but it's okay for Sarah, who is validated in both timelines and still an adult in the 1995 timeline,, who survives, and pretty much everyone since Alan might be able to reacquire some of his family's commercial assets and help rebuild the house (his old house) that the kids' aunt had just bought. As for emotional trauma, everything in the 1995 timeline is, and the people in alt-1994 are technically different people (being almost a year younger and never having experienced the effects of the game), so it's not like that's got any measurable advantage for them.

Van Pelt taught Alan the skills he would need to survive the jungle world of Jumanji
Not as an act of kindness, but with the intent of turning Alan into resilient prey worthy of being hunted. While Alan recognizes Van Pelt as a sociopath from the beginning it isn't until the hunter tries to kill him that he realizes just how sadistic he is.

Tribal Bob was once a human.
We know that Peter once became a Manji, though he was cured, there nothing saying it never happened before. All the other Manji have animal-like masks, but Bob's looks vaguely human-like, like Peter's did. Bob was once a player who got stuck in Jumanji, and became a Manji to survive. He probably didn't have anyone close to him to bring him back to his human form.

Jumanji and Zathura were created by a sadistic Eldritch being.
Someone - something - had to have created the board games in the Jumanji 'verse - something with almost Godlike power, as the games clearly have the ability to augment reality - thus this entity would have had to give them either a fragment of its own power, or be in a position to access something of such immense paranormal force. It would be easy enough to label them as creations of a fun-loving Trickster god, much like The Mask, if not for the fact that these games, while seeming like harmless paranormal fun at first, are very much intended to kill people - particularly, the children playing the game. The fact that the board games don't rack up a bloody death count stems less from their own canonical potential, and more from the fact that these movies aren't rated R (or 18+).

So the logical conclusion remains - just what cosmic horror with a creatively sadistic flair created these games? Perhaps they want man's imagination to be his downfall...

Take note that the Jumanji game must have been created in the 1800s, if Van Pelt is any judge. During the peak of the British Empire, no less. Perhaps it was a horrible punishment for what the British Empire did to a lot of African tribes. Zathura, meanwhile, has aesthetic designs which were very similar to the perception of sci-fi in the 1950s; following this line of thought, it's plausible that the same entity created Zathura as punishment for mankind's unprecedented wars in the first half of that century.

Jumanji and Zathura are the same magical artifact
It is a magical item or cursed item that appears as a game that is semi-familiar to those it encounters and wishes to ensnare. It is not one particular game, but rather a magical iem that takes the form of a game.

Van Pelt is genuinely trying to be a father-figure for Alan
Hear me out on this. He's so capitally hardened by his big-game hunter life, and, being from the time period he looks to be from, he's being a dad the only way he knows how. Imagine the upbringing Van Pelt must've had! He keeps trying to tough Alan up, telling him to "Face me like a man" - while holding a gun - and does so because it's how he was raised. In fact, Van Pelt is probably seriously scarred to the point of anhedonia, and he probably wants to carve Alan (not literally) into a version of himself. See, if he achieves this, he will finally feel the love of seeing himself in another human (and that's what love is, right?). He laughs when Alan finally does face him "like a man". This is his anhedonia melting off, slightly. So he's all up on Alan being his warped idea of tough because he's trying to be a father figure. Come on, he wouldn't be the first person to go about it all wrong. The fact that he was actually going to kill Alan is because his anhedonia (complete lack of pleasure) has made him suicidal. But a "man" wouldn't commit suicide, so he wants to kill the prodigy who's now willing to face him.