Approved Television
Fantasy
Game of Thrones: The George R. R. Martin's pet project finally made it to the small screen. Combines the epic swords and sorcery of high fantasy with the nihilistic hopelessness of actual medieval life. Thanks to Martin's amazing horrible skubtastic writing and HBO's massive budgets this show has gone a long way towards making fantasy "respectable".
Carnivale: A group of depression era carnies caught up in a Manichean struggle between the forces of light and darkness. One of HBO's first experiments with high concept, high budget fantasy. Died ignominiously after two seasons due to scripting problems, audience apathy, and grimdark overload; but paved the way for those who would follow.
Hercules: The Legendary Journeys: Concentrated nostalgia from back in the days when fantasy shows were relegated to Friday night time slots where they couldn't harm the general public. If you're a neckbeard in your twenties, this show probably had something to do with it. Kind of embarrassing by today's standards, but it pioneered everything from CGI monsters to filming in New Zealand. Resulted in it's much more famous spin off series...
Xena: Warrior Princess: Before you knew her as an uppity Cylon or an insane Roman housewife Lucy Lawless was the leather clad, god slaying, amazon OG. If you're a neckbeard in your twenties (or a ca/tg/irl who liked Gabrielle a little too much), you probably fapped to it. The cultural cache of this show is so great that even underage B& that never could have seen it will recognize the character.
Historical
Spartacus: Blood and Sand A faithful historical narrative about the third servile war and the various social pressures that precipita... phhht no I'm kidding it's wall to wall tits and ultraviolence. Despite being a relentlessly silly 300 wanna-be that had no business ever being green lit it actually managed to be a treasure trove of feels and awesome, due in large part to unusually solid writing and some heroic performances by actors like John Hannah, Lucy Lawless, Craig Parker, and Peter Mensah.
Rome It's HBO so the tits and ultraviolence spigot is still wide open, but this one actually does some good world building
Sci Fi
Babylon 5:
Farscape:
Doctor Who:
Firefly: Post-bellum Confederates, IN SPAAAAAACE. Like most of the Whedonverse praising it on /tg/ will unleash a category 5 skubstorm.
Star Trek: Is Star Trek. If you were born some time in the last half century you probably heard of it.
Comedy
Mystery Science Theater 3000: A bunch of Minnesotans with robot puppets riff on terrible movies. Achieved legendary cult classic status after being cancelled (since it confused and angered the norms) and spawned the venerable [www.rifftrax.com rifftrax].
Western Cartoons
Samurai Jack: A time lost samurai kicks ass and saves lives in his quest to get home.