Amazing Stories was what is known as an "anthology series", where each episode is new every week and has no bearing on past or future episodes.
Amblin produced it, and Spielberg's friends basically used it as a awy of trying new things or just taking time out to have fun. Scorsese, Eastwood, Dear, DeVito and Zemeckis, among many others, would all direct episodes, though they are of varying quaility (storywise).
Four of the best:
THE MISSION, directed by Spielberg, was the first season's one-hour opener, and featured a damaged bomber plane that had to crash land. One of the gunners is a cartoonist and "draws in" the third wheel that is needed to help the plan land without crushing him inside. Two years before Roger Rabbit, this had wonderfully lush, rounded animation, and with camera perspective moves too!
GHOST TRAIN, not directed by Zemeckis, but by Spielberg again, was an homage to his grandfather. The story is the same as above, with the title train coming and taking a young boy's grandpa's soul off when he dies. It's all done with great mystery and typical Spielberg goodness. This was a regular half-hour show, I think the season closer.
GO TO THE HEAD OF THE CLASS was the second season's opener, again a full hour, and this is the one directed by Zemeckis. Christopher Lloyd puts in a great performance as a rotten schoolteacher who loves to get student Scott Coffey (remember him?) in detention. When the student and his girlfriend plan an occult revenge on the teacher, they find out just what HE's made of too! A fun ride, and full of Zemeckis' bite, more along the lines of his Tales From The Crypt rather than Roger or Gump!
FAMILY DOG - anyone remember Brad Bird's short-lived Universal series? Only around 12 episodes were made, but the show actually started life as in Amazing Stories - the pilot was an episode! Featuring a typically retro-family (as seen in Inron Giant and Incredibles), the show was basically The Simpsons told through the eyes of the Family Dog. This first, rather bizarre show, features some nice comic touches, leading to the flatter, blander, sitcom-styled series. The animation here is better too, being theatrical quality (though done in a stylised way) rather than the TV quality used in thr subsequent series.
I have all these episodes (and the Family Dog show) on LaserDisc, and they're quite worth seeking out. Rumor is that Amazing stories - all 44 episodes of them - are coming to DVD in 2005, and I strongly recommend them!
Hope that helps!