There were certainly great animated TV series based on Marvel Comics properties coming out in the 80s and this one, featuring Spider-Man, one of Marvel's most prominent superheroes, is no exception. While the series definitely has a few weaker episodes, there's definitely more good ones.
While the premise is lifted straight from the comics, all of the plots are original to the series and the series balances a supporting cast of Spider-Man enemies, guest villains and original characters. A lot of the cast from the comics is present, like Peter's elderly aunt May, his choleric boss J. Jonah Jameson or Peter's love interest Betty Brant. Other characters are mentioned and lots of other Marvel characters have either guest appearances or cleverly hidden cameos.
The series is a big step up from the 1967 TV series and not only features thrilling superhero action but also very human moments like Peter's struggle with money and him trying to balance his private life with his superhero life.
In one very outstanding example, Spider-Man actually tries to help the supervillain get out of his miserable situation instead of just defeating him. Unfortunately, it is a one-time example but it definitely sets the stage for other Spider-Man series to come.
One minor issue I had when watching it was that I noticed that the series could have benefitted from a different episode order in my opinion. There's an epic six-parter with Doctor Doom scattered througout the series and a two-parter with a Kingpin and then the series just ends with a one-shot that not even contains a Spider-Man villain. The Doom episodes certainly have the feeling of a series finale and the viewer experience could enhance if the episode "Countdown to Doom" is watched last.