Approved Television

Fantasy

Game of Thrones: The GRRM'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 are 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 and political intrigue on the side.

三国 (Three Kingdoms 2010): Widely regarded as the best and most accessible version of China's most famous story (essentially their Iliad). Almost a hundred hours long, epic scope, tons of actors, and legions of extras (you can buy them by the bushel over there). Almost worth it for Chen Jianbin's gloriously dickish Cao Cao alone, but there's plenty of other reasons to stick around. The entire thing is available on youtube and elsewhere because CCTV could not give two shits about licensing it outside of the country.

Sci Fi

Babylon 5:

Farscape:

Stargate:

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 Rifftrax.

Western Cartoons

Batman: The Animated Series: In a time when most cartoons were still glorified half hour toy commercials BtAS dared to defy convention with a dark art style, darker themes, and characters you actually gave a shit about. This show was so iconic that a lot of the stuff you think was original from the original /co/ canon (Harly Quinn, Mr. Freeze's wife) actually started here.

Samurai Jack: A time lost samurai kicks ass and saves lives in his quest to get home. Elegance in simplicity.

Gargoyles: Disney's serious response to Batman: TAS (as opposed to Disney's satirical response to Batman: TAS of Darkwing Duck, which was also alright for what it was). Some Gargoyles (a race of winged strong humanoid creatures that turn into stone during the day, rather than mere architectural adornments) live in Scotland the middle ages fighting Vikings, get betrayed, frozen in stone and are re-awakened in modern New York by a buisinessman who could give Tzeench lessons in plotting played by William Riker. That is just the beginning, as there are also stories of betrayal, robots, suits of power armor, cyborgs and a fair number of magical things borrowing from a variety of mythological sources, but most notably the works of William Shakespeare.

References

One of many threads.