When Fry fell over in his chair, he actually hit his head and went into a coma or became mentally impaired where he imagined he awoke to living in the future.
The series starts off with Fry as a delivery boy that gets a prank call on December 31, 1999, New Years Eve, to deliver pizza to a closed cryogenic lab. Upon realizing he's been duped, he leans back in a chair as he counts down to the new year, 2000. His chair falls over and he lands in a cryogenic cell where he's frozen for 1,000 years.
During the 1,000 years, the camera pans outside of the window of the building to show the world aging, and ultimately evolving, including alien attacks that destroy every building in sight. When his time is up in the chamber, he's awoken by a cyclops, Lela, who informs him of the year and gives him his mandatory job of delivery boy. Upon learning he'd be stuck doing the same job in the future, he runs and meets up with his soon to be friend robot, Bender, and learns of his (senile) living great (x30) nephew, Professor Farnsworth who offers jobs to Bender, Lela and Fry to be a delivery team, which Fry is somehow excited about.
The rest of the show is comprised of going on journeys to new planets, meeting new races, and dealing with sophisticated technology typically created by Professor Farnsworth.
The physical manner in which Fry is frozen is quite odd. Not only does he fall backward and somehow lands upright in the cell, but when he lands, the door shuts, locks and the dial which sets the length of time the cell will be frozen is all done automatically. Even in the episode which shows that Nibbler tipped his chair back, the other actions involved were not done by anyone else, even though someone on the outside would have to perform those actions.
With only a few exceptions, the universally (and multi-versally) spoken language is English no matter what planet they venture to, or what alien/mutant race is met. Even with the few exceptions, such as the Carcaron race, there is a device used that translates from their language to English so that everything is understood.
His family even visits the lab where Fry is as they are in search of him, but somehow can't find him even though Fry's adopted dog is barking and clawing where Fry is. The family could not have just happened upon the lab and ignored the dog, they just could not help him out of his coma. Fry would not have known about this encounter if he was indeed frozen, since there would be no evidence considering his family did not know he was there. Additionally, any worker at the lab would have noticed the mistake and unfroze Fry, but Fry imagines a situation where he can't be unfrozen.
Perhaps the most supported evidence of this theory is being shown the world outside of the cryogenic lab being destroyed on multiple occasions, but that the lab (which hosts Fry) is kept untouched. With alien attacks, society rebuilding and needing shelter, supplies and food, the decaying properties of the building, the ground around it, the cell and the chemicals + electricity needed to run the cryogenic cells, the building could not physically be standing after 1,000 years if the buildings and society around it were destroyed as well. In addition, some items and information from the past somehow work in the future, such as the bank card reader used to retrieve Fry's 1,000 year old bank account which grew from $0.93 to $4.3 billion.
Additional Evidence Edit
There are episodes where Fry learns things from the "past" (after he was "frozen") that he wouldn't have learned on his own from being in the chamber, these are actually things that his family tells him while he is in the coma in which case he imagines a case in which his future self happens upon these discoveries by finding perfectly in-tact, fossilized evidence or some form of futuristic technology. For instance, learning that his brother married and had a son whom he named "Phillip J. Fry" after Fry himself, or learning of the outcome of the Rose Bowl by his mother with her radio (that she always has with her at all times).
This theory comes to light in the episode "The Luck of the Fryrish" when events in Fry's past life are shown to elude to the fact that Fry's dreams were to be an astronaut by showing the rocket above his crib and that his brother stole his dream of being the first man to land on Mars. Other episodes help support his imagination of a futuristic life by showing that Fry was into sci-fi which would explain all of the aliens and futuristic technology. Additionally, at the end of the episode, when Fry's brother names his son after Fry, he directs his speech to Fry as he states that he loves and misses Fry. This is a speech that Fry would only know about if he was there in person.