Based on the events of the Ghostbusters movie, The Real Ghostbusters departed from the look of the characters in the movie, but the personalities were left intact. This cartoon had a good number of well-known writers behind it (like J. M. Straczynski, just to name one) and great voice talent.
During the first two seasons it had some of the best animation of it's time, and even today it looks great. The artists also capture a certain spooky mood and atmosphere to balance against the comedy of it all, just like the movie.
From the third or fourth season onwards, the show quality dipped a bit, but was for the most part very good. Later it became "Slimer and The Real Ghostbusters" aimed at smaller children than originaly intended.
Great episodes from earliy in the show that I can remember (it's been a while) are: "Knock, Knock", "No one ever comes to Lupusville" "The Boogieman Cometh", "Ragnarok and Roll", "Doctor, Doctor", "Citizen Ghost", "Apocalyspe, what now?", "Mr Sandman Dream me a dream", "When Halloween was forever", "Ghostbuster of the year", "Spacebusters", these are the only I can remember vividly from just reading the synopsises here at tv.com.
Oh, right! and the proton-packs were never enough to catch the main ghost, so the ghostbusters always had to come up with a clever alternative way to achieve thier goal.
Other cartoons from that time are already out on DVD (He-man, Thundercats, GI-Joe, Transformers, TMNT, etc.). Why has it taken so long for this show to be immortalized in that format is a good question.