The time machine is originally created in Season 1 Episode 4, "Mind Over Murder", in an attempt to avoid the pain caused by teething.
In Season 4 Episode 30, "Stu & Stewie's Excellent Adventure" Stewie goes back in time to save himself from being crushed by a lifeguards chair which caused him to become "disgusting" as his baby self puts it.
In Season 7 Episode 3, "Road to Germany", Mort stumbles into the time machine and ends up in WW2 Germany. As such Stewie and Brian have to go in after him to bring him back.
In Season 9 Episode 16, "The Big Bang Theory", Stewie goes back in time to stop Bertram from killing Stewie's ancestor Leonardo da Vinci as Stewie created the universe with his time machine. In killing Leornado the universe would cease to exist.
In Season 10 Episode 5, "Back to the Pilot", Stewie and Brian use the time machine to go back to the first episode and then lots of future them end up going back to stop the event changes that happened.
In Season 10 Episode 22, "Family Guy Viewer Mail No. 2", Stewie uses his time machine to prevent Kurt Cobain from killing himself.
In Season 11 Episode 4, "Yug Ylimaf", Brian is using the time machine to pick up girls and ends up reversing time. Stewie then uses the time machine to set everything straight again.
In Season 12 Episode 8, "Christmas Guy", Stewie uses the time machine return pad from a past Stewie, who had travelled forward in time, to go back in time and save Brian.
In Season 12 Episode 21, "Chap Stewie", Stewie uses a time machine to change himself to be born to a British family. After realising he prefers his previous life he builds another rudimentary time machine to change things back again.
In Season 13 Episode 7, "Stewie, Chris & Brian's Excellent Adventure", Brian and Stewie take Chris on a journey through time to try and teach him enough to pass his history test.