Roswell that Ends Well is the first episode in the 4th broadcast Season of Futurama. This episode won the 2002 Emmy for Outstanding Animated Program (For Programming Less Than One Hour), the show's first Emmy.
The crew is sent back to the year 1947 when Fry puts metal in the ship's microwave while the rest of the crew is watching a supernova explosion. The resultant reaction causes the ship to vanish into a tunnеl, where they pick up a number of clocks before exiting out a portal. Confused, the crew decides to head back to Earth, only to find no space traffic. Worse, there is no receiving signal, so they crash land in Roswell, New Mexico, causing an unsecured Bender to fly into pieces. While everyone else, including Bender's head, heads back to the ship, Zoidberg is left picking up the pieces. However, at night he is found by the U.S. military. The next day, the crew realizes that the famous crashed UFO that brought Roswell, Area 51, and the related conspiracy theory into popular culture was in fact them. The Professor then explains that the microwave's radiation and the gravitons and graviolois from the supernova blast them through time itself.
The U.S. military kidnaps Dr. Zoidberg, who was gathering up pieces of Bender's body, and takes him and Bender's body to Roswell Airbase to conduct various experiments, including an alien autopsy and 'UFO reconstruction'. President Truman also arrives to interrogate Zoidberg on either if he comes in peace, staging an invasion or creating a hybrid, but Zoidberg's people skills have him vivisected. "No one is to know about this except the senior officers, scientists and a single nutcase reporter no one will believe."
While the crew looks for another microwave, which they can't find in Roswell, Fry and Bender's head infiltrate the army base. Fry then encounters his grandfather, Enos Fry, who is stationed at the base. As Professor Hubert Farnsworth had previously warned Fry about causality and the fact that if his grandfather dies, then he will never exist, Fry becomes obsessed with protecting Enos from any possible harm. However, his fear and paranoia result in him overreacting to minor threats and putting Enos in far more danger than he would have been otherwise. He is even more alarmed when Enos exhibits signs of latent homosexuality, making it look unlikely that he will actually father Fry's father. Inadvertently, Fry brings about Enos's death, by leaving him in a "safe" house on a nuclear weapon test range.
Leela notices that there is microwave dish from the Roswell Airbase and suggests that they steal it but the Professor says that they can't screw up the past in anyway possible. Fry then turns up to inform everyone that he killed Enos. Leela points out that if Enos is dead, then why is he (or given their kinship the professor as well) are still in existence, a question that Fry can't figure out. He then consoles his would-be grandmother Mildred, who was at the time engaged to his grandfather. He deduces that since he is alive, the man who died in the nuclear blast could not have been his grandfather. This leads him to believe that Mildred could not be his grandmother. Mildred then seduces Fry and they end up having sexual relations. The next morning, Fry discovers, with the prompting of the Professor, that Mildred is indeed his grandmother, due to the fact that she looked and acted like an old lady. Fry actually becomes his own grandfather, and is now the father of his own father Yancy Fry, Sr., making him freak out (though this saves Fry and the Professor and keeps them in existence).
Ultimately, Farnsworth gets fed up with causality and decides to steal the dish anyway. They attack the base with the ship, outclassing the 1940s tanks with their superior weapons. Fry and Leela rescue Dr. Zoidberg, with the latter beating up the men performing the vivisection and Fry throwing Zoidberg's organs at Truman; the Professor picks up Bender's body which was due to be sent to Area 51 for study; since this was where the fake Moon landing was to be filmed, Truman invented NASA to land on the moon for real. But as they prepare to travel back to the future, Bender's head accidentally falls out of the Planet Express ship before the time warp, and is left behind in the year 1947. Back in the 31st century, Zoidberg has all but one non-essential organs in him. Fry laments about the loss of Bender, but then hits on a brainwave and the Planet Express crew finds him in the approximate physical location of the Roswell Airbase around the Roswell desert in the 31st century, and re-attaches him to his floating 'UFO' body.