The Forwards Time Machine was a temporal navigation device invented by Professor Farnsworth in 3010. The machine is only capable of traveling into the future, specifically in order to avoid creating temporal paradoxes such as accidentally having sex with one's grandmother. However, this purpose finally failed, as a consequence that, in the series, the time is cyclic, what means that the universe can start again, allowing make changes in any moment of history in which machine stops.
Bender, Fry and Professor Farnsworth initially intended to test the machine by traveling one minute into the future. The Professor slipped while manning the control panel however and inadvertently transported to the year 10000. Because the machine had no reverse-time-traveling function, the three were marooned in the future until they decided to continue further down the timeline, hoping that a Reverse Time Machine would eventually be invented.
Bender, Farnsworth and Fry then proceeded to use the machine to travel to several points in the future, including the years 105105, 252525, 351120, 1000000½, 5000000, 5000005, 10000000, and 50000000. The three eventually reached the year 1000000000, at which point the Earth had become a desert wasteland devoid of any trace of life.
Realizing that a Reverse Time Machine would therefore never be invented, Farnsworth, Bender and Fry decided to travel forward to the end of time, watching the death of the universe in the process. They eventually reached the last moment of time at 100000000000000000000000000000000000000000000000000 and witnessed the expiration of the universe, after which they were stunned to see the Big Bang occur again.
They then watched the universe form anew and traveled forward through history toward the moment in 3010 when they left the original timeline. The Professor slipped again as the machine neared the correct moment and the three were forced to continue into the future again, to the end of the universe, through another Big Bang and back to the year 3010.
Sometime afterwards, Farnsworth modified the machine so it can travel backwards in time. He used it again in the year 3023 in order to fix what made Robot Santa evil. So he used it to travel back to the year 2801 and reversed Robot Santa's Naughty-Nice Sensor, not knowing that said sensor was right the entire time. He tried moving forward back to the present, but he slipped and ended up going further backwards, prompting him to witness the Big Bang of the current universe and the death of the universe before that in reverse before making it to the 3023 of that universe.
Later on, both Bender and Zoidberg decided to use the time machine in order to ruin everyone else's Christmas by going to last Xmas and kidnapping Robot Santa there. So they do so, not knowing they actually traveled to the Xmas of the current year instead of the previous Xmas. After Robot Santa broke out of his confinement, Bender tried stopping him by throwing the time machine on him, only for Robot Santa to tear it apart with his bare hands.