In the Futurama episode "The Late Philip J Fry" they travel forward in time to the heat-death of the universe, and even further until a new Big Bang spontaneously occurs and they loop back to the year they started from.

Twice.

According to Wikipedia, the estimated time frame for quantum fluctuations to create a new universe is 10^10^56, so we can estimate that they travelled 2 x 10^10^56 years into the future. Read below for why this is very probably not true.*

To give an exact date: They traveled to the year 3010, two universes into the future.

EDIT: To answer some questions from the comments, the oldest mentioned year from the episode is 1x10^40 AD.

Since they are traveling through time, and the time machine is counting the exponents, they were definitely exactly in the year 10^40, even if only for a split second of their time.

*As for the estimate of 10^10^56 being the last year they are at due to the idea that quantum fluctuations caused the new Big Bang is just speculation due to the cause of the new Big Bang not being specified. However: Going frame by frame through the video as the year counter is ticking, the time machine is ticking through time exponentially at a constant rate of 10 frames per +1 exponent. The time machine seems to be going faster the longer it runs, at least in the old universe, and counting the amount of frames between the frame it counts 1x10^40 to the frame the new Big Bang happens (336 frames afterwards), the best estimate we can get to the farthest they got into the future is around 10^(40 + 33.6) or 10^77.6, which would make way more sense given the speed they were shown to be traveling. If this is even in the ballpark of true, then even if they continued at their exponential acceleration they would have to spend longer in the time machine than the universe took to die to reach the year 10^10^56.

Man, exponents are cray-cray.