Yu-Gi-Oh!: Bonds Beyond Time/WMG

The warning applies here as well. HERE BE SPOILERS!

Paradox is a Time Lord.
Obligatory Time Lord WMG to start this off. His D-Wheel, obviously, is his TARDIS. There is also to note that the future was utterly destroyed and there's no way anyone would have survived the destruction. Thus, Paradox did actually perish at that time and regenerated into the form we have seen him as in the movie, as well as gain the current outfit, which is considerably more clean compared to the circumstances. Upon witnessing the desolate world as he had no memories of his previous incarnation, he was struck by grief which he then carried on his shoulders, and was determined to correct the world, no matter what the cost. He ultimately faces the three protagonists in a duel. However, the destruction of Sin Paradox Dragon puts him into a pinch, which forces him to go through a Meta Crisis, fusing himself with Sin Truth Dragon to gain an upper hand and keep the monster in stable control. He disappeared when Stardust Dragon destroyed the fused being. This hybrid Paradox may or may not have regenerative powers. With the scriptwriter stating that Paradox is connected to 5D's, we will be either seeing the same person or a regenerated one.

Paradox came from
We're talking about the distant future here. The future has been somehow destroyed to the point that Paradox is the only human alive, or the only survivor in the vicinity. There are only ruins left of the civilization, there are no seas or forests, and the Earth is completely red, similarly to the bad ending of Chrono Trigger. Paradox knew the future was destroyed because of Lavos Duel Monsters, so he traveled back in time to change the past. Furthermore, his D-Wheel was made from the union of Johnny and the Epoch. From Johnny the vehicle gained its transforming capabilities, and from Epoch it gained its floating ability as well as the power to travel across time.

Paradox is responsible for all the continuities.
The anime,the 4Kids dub,Season Zero,the manga,even the Abridged series...all are different timelines that are the result of Paradox trying to change the past.

Duel Monsters is Spiral Power and Paradox is a human converted by the Anti Spiral.
The Synchro Monsters are the representation of evolution, and Yugi and Judai used cards called Neos Spiral Force and Black Spiral Force. According to Paradox, Duel Monsters was responsible for the world's destruction, and he wishes to travel back in time in order to destroy it. He also tells the protagonists humans continue destroying their world and the world must be corrected. When Yusei explains the future can be changed and people can change as well, Paradox says his answer is nonsense. At one point, he taunts the protagonists they are overcome with absolute despair.

Paradox is the shadowed, unidentified member of Yliaster seen twice during the Dark Signers Arc.
Word is Paradox will appear in future episode of 5D's, and this other guy's name and motives have yet to be revealed.

Paradox is Paradox.
This movie must take place during his period of madness, before he grew literally Bored with Insanity.

Yusei has his own "Spiral Force" card...
...called "Star Spiral Force", judging from the names of other two and Majestic Star Dragon.

Paradox is related to Hiruma.
They are voiced by the same person, their laughs are similar, and they both outwit others in their own dirty way. They are also willing to do whatever it takes to reach their goals. Outside the movie, Paradox hacks the JumBANG! broadcast, fools the cast and even mocks them in the end. In the movie, he steals Yusei's Stardust Dragon and even rubs the fact in his face. And while Hiruma is very fond of guns and his slaves, Paradox has his giant motorbike and personal dragon horde. Or seeing how the movie didn't reveal Paradox's identity, it could be possible he is Hiruma in disguise.

The Bad Future Paradox came from is the same future that Darkness showed Judai at the end of Yu-Gi-Oh! GX
Just look at the scene where Darkness shows Judai/Jaden the ruined future of the world and compare it to the scenery that Paradox Looks at at the begining of the movie. It makes sense in context.

Paradox stole Kaiba's coat.
THAT JERK!
 * Or it's actually Mokuba that stole his brother's coat.

The Shadow Games/Games of Darkness/whatever the fans are calling them this week were created by Sigereth in order to further the Reclamation.
Sigereth, for those unfamiliar with Exalted, is a powerful demoness known by the sobriquet of "the Player of Games". As the title implies, her powers revolve around challenging people to games of chance and/or skill for ridiculously high stakes--think memories, skills, you body and soul...Sound familiar, anyone? Demons in Exalted are basically Sealed Evil in a Can--and the only way to break the seal for good is to corrupt the mortal realm until it's indistinguishable from the demonic one. Accordingly, Sigereth introduced the Shadow Games to the Yu-Gi-Oh world, knowing that the immense power inherent in them would be an enormous temptation to anyone who knew of their existence. The scary part is, her plan seems to be working--the Yu-Gi-Oh universe is getting steadily Darker and Edgier with each new installment, and this seems to coincide with how widespread Duel Monsters becomes among average people...
 * Clearly, Paradox's future is one in which this plan has succeeded.

Paradox is Jack Atlas.
Think about it, why would Paradox go back to Yusei's time first instead going to Jaden's or Yugi's time. The answer he gives is that he is going back to kill Pegasus and create a future without duel monsters, so he stops here first and steals Stardust Dragon. Now why would Paradox do that? The answer is simple he has done it before. In the future sometime after the end of the World Riding Grand Prix, Akiza, Leo and Luna decide to go and finish duel academy and graduate. Soon after this happens Bruno decides to leave also and go back to using his secret idenity of Dark Glass. Well weeks go by, until one terrible day Yusei and Crow are out turbo dueling each other when a thunderstorm comes up. Well instead of listening to Jack Atlas, they decide to finish their duel and both end up getting killed by lighting. After their deaths, he starts to believe that if Pegasus never created duel monsters then Yusei and Crow wouldn't have died. So that is the reason why he steals Stardust Dragon. Now my general reasons as to why Paradox is Jack Atlas from the future are number one, Paradox goes back and steals Stardust Dragon first. Well, like I said before he has stole the card before and this happened two years before Yusei enters New Domino without a permit (it's against the law there). Also his hair, cape and motorcycle are similar to Jack Atlas's hair, cape and motorcycle. So just think about it. Oh and here are pictures of both of them for you to compare, first and then.

Card Games are going to bring about the end of the world.
The whole Signers Vs. Dark Signers will get out of hand that the entire world will hang in the balance and the heroes will lose.

The Bad Future wasn't caused by Synchros; it was caused by Tuners.
If the problems was a power creep due to an easy and quick way to summon a powerful monster, than Exceed Monsters would also have the same problem. But There is a difference between the two types of cards: Synchros need Tuners, but Exceeds use just normal kinds of monsters. Therefore, it wasn't what Synchros could do in-game that was their problem, but something like a curse on the Tuners they rely upon that made Bad Things Happen.

Paradox was the cause of his own apocalyptic future and would have caused a Stable Time Loop because You Already Changed the Past had the protagonists not interfered.
Unbeknownst to him, Paradox's actions while time traveling caused the very future he was trying to prevent. By stopping him, the 3 protagonists erased that timeline and saved not only their own presents but the far future. There, they've been acquitted of sacrificing one civilization in the future to save the civilizations of their presents.

This takes place, for Yugi, before his duel with Judai shown in the Yu-Gi-Oh! GX finale.
When Yugi duels Judai at the end of GX, he calls the latter "Judai-kun" without ever being told his name. He must have recognized him as one of the time travelling duelists he once met, but, of course, didn't tell him so for fear of screwing up the future.