Answer: Dr. med. Who
As far as sci-fi series go, Dr. Who is a true Methuselah. The show, focussed on The Doctor (a humanoid alien with extraordinary powers) and his intergalactic adventure, first aired in the UK in 1963. It ran for 26 seasons and ended in 1989. In 1996, there was a TV movie, and then, in 2005, the show was revived. The show is still aired as it is being written and has aired over the course of the original and ongoing running runs, incredible 840+ episodes.
If you wanted to catch up on each episode, you would have to take about two months off the job and log stable layers of Dr. Who 7 days a week. Unfortunately, it was impossible to catch up with the entire series because, due to poor archival practices at the BBC prior to 1
Other noteworthy long-running sci-fi series include Star Trek (741 episodes across 6 TV series and 1 animated series), Stargate (380 episodes across 3 TV series and 1 animated series), Smallville (217 episodes) and X-Files (218 episodes)
Courtesy of the BBC.