The Classifications or classes in the cartoon seem to vary from the film and Ghostbusters Role-Playing Game Classification System. The power of the entity seems to be the base of the scale, and the scale seems higher than the Role-Playing Game (RPG) version. Although, the classifications from the RPG do roughly scale upward in terms of power. According to J. Michael Straczynski, he stuck to the conventions of the first movie and variations in classifications were ad-hoc, rather than being anything systematized.
In the cartoon, the system ran on a Class 1 to Class 13 scale, with 13 being the strongest and least likely to see. Various books, such as "Tobin's Spirit Guide" and "Who's Who in the Spirit World," served as the basis for the Animated Classification system.  
In The Real Ghostbusters episode "Ghosts R Us," the Ghostbusters encountered a Class 10 Toy Ghost that inhabited the abandoned toy factory chasing off the Class 7 Turlock. Class 10 ghosts and higher are considered extremely rare.
The Boogieman was identified as a Class 7 Corporeal Entity. Hob Anagarak was stated to be at least a Class 7, but could not be precisely measured due to a P.K.E. Meter overload (it is also possible his prison reduced his emanations).
The Player, Mee-Krah, the Ghostmaster, and the Master of Shadows are all much stronger than a Class 7 ghost. In the Extreme Ghostbusters episode "The Unseen," the Ghostbusters encounter a Class 13 ghost named Tenebraug. Tenebraug is the strongest ghost by the scale, the Ghostbusters have encountered yet. It is unknown if there is a cap to the scale of the ghost classification system. However, entities such as Cathulhu were noted to be beyond the standard scale.
In Marvel Comics Annual 1990, they used a classification system similar to the one used in the Role-Playing Game, except a Class 6 entity was described as being close to a Class 7. Also, while the class system in the comic only goes up to Class 7 like in the movies, Ray mentions he is off to bust an unlisted Class 9 in the introduction.
Class 1s are the weakest type of ghost, being non-sentient and almost completely harmless manifestations. The only known Class 1 was the Class One Poltergeist, which briefly appeared in an issue of the NOW comic book.
Class 2s are described as being very weak entities. The only known Class 2 were the Pallo Mansion ghosts and a Class 2 that the original Ghostbusters encountered in the linguini of a client named Mrs. Fiorini before their vacation at the Stantz Dairy Farm. 
In the animated canon, Class 3s are relatively stronger than Class 2s.
Examples of Class 3's:
In the animated canon, Class 4s are creatures relatively stronger than Class 3s, though they are also described as being roughly similar to Class 5s.
Examples of Class 4's:
Much like in the movies, Class 5 ghosts are vaguely humanoid in appearance and often slime things.
Examples of Class 5's:
Class 6 ghosts are pretty powerful with some level of godlike powers. Similar to the role-playing game, certain Class 6 entities are ghosts of animals or animal-like ghosts.
Examples of Class 6's:
Similar to the role-playing game, Class 7s are very powerful entities with god-like powers. Within the animated canon, it is possible to trap and contain a Class 7.
Examples of Class 7's:
Class 8 ghosts are slightly more powerful than Class 7s. They tend to consider themselves superior over others and are usually demons. Like Class 7 spirits, Class 8 entities can be captured in ghost traps.
Examples of Class 8's:
Class 9 spirits are even more powerful, so much that they are very difficult to trap if possible. The only known Class 9s were Simon Quegg's Horse and Buggy and a Class 9 Free Roaming Vapor that manifested at Gracie Mansion during the Proteus incident. 
Class 11 ghosts are extremely powerful leaders of lesser ghosts. The only known Class 11 entity was the Ghostmaster. Ray originally thought it would be impossible for the traps to hold a Class 11. However, they managed to trap the Ghostmaster after he expended too much of his personal power.
A Class 13 is the highest known Class level, only used in Extreme Ghostbusters. The only known Class 13 entity was an eye-stealing demon named Tenebraug.
Since it is never stated exactly how many classes there are in the animated series, there may be even more Classes. There are also some ghosts on the show whose classes are not given, as well as ghosts whose power is beyond the standard class system.
Examples of Ghosts with Unknown Classes:
Examples of Ghosts beyond the standard Class System:
- The first mention of a Class 9 was not in any of the animated series but in the novelization of the first Ghostbusters movie. In Ghostbusters: The Supernatural Spectacular, Peter Venkman purposefully released a Class 9 Autonomous Roaming Disrupter in the offices of The National Reporter because of articles that smeared the Ghostbusters as fakes and charlatans.
- In Marvel Comics' The Real Ghostbusters Issue #3, relatively early in the history of the franchise, the "Spengler's Spirit Guide" section uses a reversed classification system, where a "basic class nine spook" is the weakest and a "class one special category super-hostile phantasm" ranks towards the top.
- The Mega-Entity in Ghostbusters 35th Anniversary: The Real Ghostbusters was a Class 99.
- straczynski Tweet 5/6/19 J. Michael Straczynski says: "Pretty much sure I mainly stuck to the conventions from the film. If there were variations they were all pretty much ad-hoc, rather than being anything systematized."
- "Halloween II 1/2"
- "Revenge of the Ghostmaster"
- Ray Stantz (1990). NOW Comics- "The Real Ghostbusters Volume 1 Issue #12" (1990) (Comic p.3). Ray says: "No, Egon! That's a Class One Poltergeist! It took us five hours to trap!"
- Winston Zeddemore (2009). The Real Ghostbusters - "Dairy Farm" (1987) (DVD ts. 1:22-1:24). Time Life Entertainment. Winston says: "And the Class 2 in Mrs. Fiorino's Linguini."
- Ray Stantz (2009). The Real Ghostbusters - "Dairy Farm" (1987) (DVD ts. 9:21-9:23). Time Life Entertainment. Ray says: "I wouldn't rule out a Class 2 Area Aberration."
- Ray Stantz (2009). The Real Ghostbusters- "Janine Melnitz, Ghostbuster" (1987) (DVD ts. 08:55-08:59). Time Life Entertainment. Ray says: "Gracie Mansion. It's being haunted by a Class 9 Free Roaming Vapor."
- Mueller, Richard (August 1985). Ghostbusters: The Supernatural Spectacular, pp. 154-155. Tor Books, New York NY USA, ISBN 0812585984.
- Egon Spengler (1988). Marvel Comics- "The Real Ghostbusters Issue #3" (1988) (Comic p.8). Egon Spengler writes: "It's difficult to say for sure where it comes from, but one may suppose that the residue is the product of extra-dimensional material (which could be anything from a basic class nine spook to a class one special category super-hostile phantasm) coming into contact with our plane of existence."
- Egon Spengler (2019). IDW Comics- "Ghostbusters 35th Anniversary: Ghostbusters" (2019) (Comic p.16). Egon Spengler says: "The ghosts from the Prediction Engine have combined into a Class-Ninety-Nine Mega-Entity."