I remember that as a kid, I used to stay up late to watch anime from Star World, a Chinese channel from cable. While they didn't feature a lot of anime, they did feature a lot of classics. Here's a nostalgia trip of the ones that struck me the most:
Ranma 1/2 - I'm sure everyone has heard about Ranma 1/2, considering it was also important in the anime revolution in the US. It was airing at 10 pm, and so I had to stay up late and watch it. A friend and I deliberated on questions such as if Ranma gets pregnant in female form, what happens when he reverts to a guy?
Saint Seiya - I honestly only caught this because it came after Ranma 1/2, thus depriving me of sleep as the show ended at 11 pm. It pioneered the genre of boys-in-armor, and became the basis for derivatives like Samurai Troopers (Ronin Warriors in the US) and Shurato. While they showed all 100+ episodes, I only caught the latter half (at this point, Athena's Saints were fighting the gold cloths).
Shurato - It's a lesser-known derivative of Saint Seiya and used "soma" as the basis for its mysterious energy. I caught the series from start to finish, rushing back home from school to catch it.
Captain Tsubasa - If there's a reason why Japan made it to this year's World Cup, this anime/manga series is responsible for it. Anyway, I caught the Captain Tsubasa J series which aired during weekday afternoons. Again, it was important for me to get back home from school to make it to its 4:30 pm time slot.
Tekkaman Blade - I first caught the series when I was visiting Canada under the name Teknoman, but sadly, they didn't finish dubbing the entire series (it ended at a cliffhanger, when a certain someone died). Was fortunate to catch it on cable during the weekends, and I finally saw the tragic conclusion (and explanation) of this mature series. It was a remake on an older Tatsunoko series, Tekkaman.
Of course there were other anime shows played over the years, but they never really it to mainstream consciousness. There was Zillion, for example, which should have been the real Lazer Tag cartoon (they had the same weapons and guns, albeit a more mature and believable plotline). Then there was this kiddie Saint Seiya clone that had a phoeix, dragon, hydra, and a female character as the source of its characters powers. It had this interesting, if somewhat cheesy ending. The cosmology of the series had four planets representing a different element, and in the end, it got combined to form... the Earth. Oh, and I think I remember watching Southern Cross and Mospeada (of Robotech fame) as well.