Good Sci-Fi shows?
Doctor Who - Is very divisive. You either love it or hate it, but I think it is the greatest TV show ever created.
Start watching from the 2005 Series where it restarted after a 25 year hiatus. Up to 6+ season now, with about 13 episodes + 1 special per season.
Babylon 5 - Great sci-fi show with equal parts diplomacy, action and social commentary. Complete at 5 seasons.
Andromeda - Complete at 5 seasons. About a captain of a ship from a fallen monarchy who comes out of stasis 300 years after the fall. Show is about him trying to rebuild the commonwealth.
Farscape - Complete at 5 seasons. About a human astronaut who enters a wormhole by mistake and ends up joining a crew of aliens in their giant living ship.
Red Dwarf - Hilarious space sitcom/comedy. At 9+ seasons (with 6 episodes per season). Cast includes, the last human alive, his annoying best friend who is now a hologram, a cat that has evolved into a humanoid form after millenia, the ship's AI and a robot.
Futurama - Really funny sci-fi cartoon from the makers of The Simosons. 6 + seasons and running.
Cowboy Bebop - Great sci-fi anime, complete at 26 episodes.
Ghost in the Shell: Stand Alone Complex - Awesome Sci-Fi. An anime that greatly inspired many things in the matrix world. Maybe the most "hard sci-fi" of the shows I have listed.
The Prisoner (the original series) - Part psychological thriller, part Sci-Fi. Complete at 17 episodes.
Life on Mars - Great series but could be considered speculative fiction as opposed to full on Sci-Fi.
Eureka - Current day sci-fi set on earth. Still running but is about to end after the next season. Good fun but wouldn't classify it as great sci-fi.
I'll add more when I remember them.