A time machine is a device that allows the user or users to go forward or backwards through time and space.
A time machine is first used in "Mind Over Murder" when Stewie Griffin originally creates it to avoid teething but ends up going back when people copy his plans, which erases the events of the episode.
In "The Courtship of Stewie's Father", Stewie sets up a cutaway parodying Doc Brown at the end of the first film in the flying Delorean time machine telling Marty and Jennifer that they have to come to the future to fix their kids' situation.
In "Stu & Stewie's Excellent Adventure", the third segment of Stewie Griffin: The Untold Story, Stu Griffin, who is Stewie at 30 years old, uses a time machine in the form of a wristwatch to go on his vacations.
Peter drives the Delorean time machine in "The Perfect Castaway".
In "Road to Germany", Mort Goldman mistakes Stewie's new walk-in time machine for a bathroom stall. He lands in Poland on September 1, 1939, the beginning of World War II. When Stewie and Brian realize this, they go in to rescue him. This model is uranium powered.
In "The Big Bang Theory" Bertram used the time machine to try and kill Leonardo da Vinci, Stewie's ancestor in order to remove Stewie from the universe. However this in turn would have destroyed the universe so Stewie and Brian go back to prevent him from succeeding.
In the "Point of Stew" segment of "Family Guy Viewer Mail No. 2", Stewie uses the time machine to travel to April 5th, 1994 to stop Kurt Cobain from killing himself by convincing him to eat lots of Häagen-Daz ice cream. In the present, Kurt is still alive but is morbidly obese.
In "Internal Affairs", Peter and Ernie The Giant Chicken fight their way onto Stewie's time pad and end up colliding with Marty McFly and the Delorean time machine in 1885 in Back to the Future Part III.
In "Yug Ylimaf", Brian uses Stewie's time machine without Stewie's permission to pick up women. To try to avoid getting caught, he attempts to reset the chronological gauge on the machine, but this ends up destroying the machine and reversing the flow of time.