Scooby-Doo (or any of the Hanna Barbara shows for that matter) never really paid that much attention of continuity. Pretty much each season had its premise and the show remained consistent with that premise. Yet, for a variety of reasons, different continuities have developed over the years.
It seems that Scooby-Doo, Where Are You, which established the mystery solving teenagers and their dog premise has taken place in some form in all continuities. It gets a bit more complicated than that.
The original 16 year run, 1969-1985, and the three Superstar 10 movies should be considered one continuity. While the premise, particularly during the Scrappy years, has changed, sometimes wildly, from season to season, the individual series don't really contradict each other. They also set up the basic outline of how events play out in future incarnations: the gang gets together and start solving mysteries, they break up for awhile, then they get back together to solve more mysteries where the stakes get higher. Heck, you could look at the original run as a character arc for Scooby-Doo, even though it wasn't intended that way. The series started with a somewhat cowardly dog who reluctantly solved mysteries but was always there to rescue his friends whenever they needed him in Where Are You to the burned out adventurer who wanted a break from ghosts and goblins that appeared in the 13 Ghosts.
1988's A Pup Named Scooby-Doo was a prequel to Scooby-Doo, Where Are You that was a tribute and a parody of that series. This introduced younger and exaggerated versions of the gang to increase the comedic value. While it does fit into the original series timeline, it's hard to reconcile the A Pup Named Scooby-Doo versions of the characters with the versions that appeared in the original run, particularly Fred and Daphine. It could fit within the original continuity but a lot of people ignore it for that reason.
The DTV's started with Zombie Island and that movie established that they solved mysteries for a few years then they broke up and went their separate ways. While that's the basic timeline of the original series, the details are quite different. The classic timeline has Shaggy and Scooby doing odd jobs with Scrappy, Daphine becoming a magazine reporter, Fred becoming a novelist, and Velma becoming an assistant scientist with NASA and the whole gang being aware that the occult is real. Zombie Island has Shaggy and Scooby doing odd jobs, Daphine becoming a television reporter with Fred as her cameraman, and Velma working in a mystery bookstore, and the gang being unaware that the occult is real, plus no mention of Scrappy. This indicates that the 1969-1978 have taken place. You could also argue that the first Scrappy season in 1979 is also in continuity with Zombie Island despite no mention of him since that season is essentially a continuation of the 1978 only with the inclusion of a new character. Nothing indicates that Scrappy doesn't exist, only that post-1980 Scooby-Doo, when occult elements started showing up, didn't happen.
Zombie Island started a series of DTV's where a post-reunion adult Scooby gang started solving mysteries again, often for Daphine's TV show. This premise lasted for the first four movies. The second of these movies introduced the Hex Girls, a rock band using a witch gimmick. Their introduction and subsequent reappearance on What's New Scooby-Doo provides the first real continuity contradiction.
What's New Scooby-Doo started in 2002 and the hook for this show was the original mystery solving teenagers and their dog premise only updated. The show ignores the premise of the DTV's, the adult gang reuniting for more mysteries, and reset them as somewhat older than they were in Where Are You but not the adults they were in the early DTV's. In other words, the gang never broke up after the events of the Scooby-Doo Show, they just kept on solving mysteries. That's fine but one episode they met the Hex Girls again. The Witch's Ghost was never referred to, only that this was not the first meeting between the groups.
Also, the personalities of the gang were broadened and played for laughs. Velma became a snarky know it all, Daphine became an action girl, and Fred became a dumb jock. Ironically because of this, it was easier to reconcile the characterizations of A Pup Named Scooby-Doo with the What's New version of these characters. Plus there was one episode that had a flashback that used A Pup's designs (although the characters were younger than they were presented on that series), thus a lot place A Pup Named Scooby-Doo in What's New Scooby-Doo continuity.
After two DTV's that used the original character designs and original voice actors in two "Where Are You" flashback adventures, the DTV's started following What's New continuity instead of Zombie Island continuity.
Shaggy and Scooby-Doo Get a Clue is a sequel to What's New focusing on Shaggy and Scooby-Doo finding their independent heroes away from the rest of the gang against the evil and insane Dr. Phibes. This follows What's New and since Shaggy and Scooby became more independent as a result of this series, the gang dynamic that takes place when they do get back together is different from "Fred tricking Shaggy and Scooby into the mystery" dynamic in most of the other incarnations. Also, note that Fred, Daphine, and Velma continue to solve mystery after Shaggy and Scooby leave, which is a departure from traditional Scooby lore.
The DTV's continue following What's New but ignores Get a Clue even while that show was still on the air. The only real difference between the DTV's before Get a Clue and after is the greater emphasis on Shaggy and Scooby's antics. The gang dynamic is the same as before Get a Clue. This suggests one of two things, these mysteries takes place before Get a Clue or Get a Clue is an alternate future of What's New.
Scooby-Doo, Mystery Incorporated seems to be another reboot of sorts. Scooby-Doo, Where Are You (at least the first season) seems to be in canon but everything else haven't taken place (yet). The gang seems younger and the town they live in is named Crystal Cove instead of Coolsville. The basic premise of mystery solving teenagers and their dog is kept but the producers are set on writing their own Scooby mythology. It also seems that the DTV's, starting with Abracadabra-Doo is rebooted as well. It's not using What's New continuity but it is not following Mystery Incorporated continuity either, rather it is telling it's own stories without being burdened by past or present continuity. Spike Brandt and Tony Cervone are overseeing both the movies and DTV's and I guess they feel that story is what comes first.
To summarize, here are what I see as the Scooby continuities:
1. Scooby-Doo, Where are You to the Superstar 10 movies (Scooby-Doo and the Reluctant Werewolf) 1969-1988
2. A Pup Named Scooby-Doo, What's New Scooby Doo, Shaggy and Scooby-Doo Get a Clue, and DTV's Scooby-Doo and the Loch Ness Monster to Scooby-Doo and the Samuari Sword (1988-1991, 2002-2009)
3. Scooby-Doo, Where are You to Scooby and Scrappy-Doo, Scooby-Doo in Zombie Island to Scooby and the Cyber Chase (1969-1979, 1997-2001)
4. Scooby-Doo, Mystery Incorporated (2010-)
5. DTV's Scooby-Doo! Abracadabra-Doo, Scooby-Doo Camp Scare (2010-)
You could take out or put in Scooby and Scrappy-Doo, A Pup Named Scooby-Doo, Shaggy and Scooby Get a Clue, and the DTV's Legend of the Vampire and Monster of Mexico as you see fit. I guess there is at least five continuities, maybe more.