Almost every Scooby-Doo mystery was scifi/fantasy until they were debunked in the end. In all of the Scooby-Doo episodes and movies or comics (excluding anything with his nephew in it) is there even a single instance in which the original gang of meddling kids in Mystery, Inc. solve something that was supernatural or real?
Yes, they did. I'm not sure of the details but Scooby saw the real Loch Ness monster after the gang solved the mystery.
Yes. In Scooby Doo on Zombie Island, they encounter real undead and werecats. In digging deeper, most of the direct-to-video Scooby Doo movies in this era also feature real supernatural creatures.
Scooby Doo (2002) featured real demons. Scooby Doo 2, Monsters Unleashed contained real monsters, although they were brought to life through "scientific" means and might not really fit the bill as "Supernatural".
In the original series, episode 16 "A Night of Fright is No Delight," the gang catch the two giggling green ghosts who are revealed to be crooked lawyers. However, at the very end they encounter a floating bone which appears to be genuinely supernatural. Fortunately this is the one type of ghost that Scooby isn't afraid of and he promptly chews it.
Obviously it's a silly joke but there's no indication that it isn't real and the gang don't seem particularly surprised at proof of ghosts.
On the sci-fi side of things, Scooby-Doo and the Cyber Chase had them fighting a "computer virus" (blue guy who lives in a computer), in cyberspace (VR, sort of?). Although the virus does put on a number of themed outfits throughout the story, none of them really qualify as disguises because they fool neither the audience nor any of the characters. So in this sense, he may be described as "real" because he was not wearing a disguise and was not unmasked at the end.
Note that any resemblance to actual computer science (or indeed physics) is purely coincidental. This is very far on the soft end of the sci-fi scale.
In addition to the previous answers, there's also a newer animated Scooby Doo TV series called Scooby-Doo! Mystery Incorporated (TVTROPES WARNING TvTropes page), contemporary with your question, which has supernatural elements. The original team of five looks into the mysteries of the town of Crystal Cove, and eventually uncover supernatural elements. I haven't watched this series and don't know much about the story, but apaprently extraterrestrial aliens are involved.