Adventures of Sonic the Hedgehog (AoStH) - The show where the "Sonic says..." Internet fad originated from. It is also what the Puyo Puyo game, "bee-hived" Dr. Robotnik's Mean Bean Machine is based on.
SatAM - The one based on the comics by Archie.
Sonic Underground - The sequel to SatAM.
Sonic the Hedgehog: The Animated Movie - I have to count this, because it's animated.
Sonic X - The only television anime series based on the video game series.
In my opinion, I would say Sonic X, because it has more characters that actually appear in the video game series than the other animated shows and movie. I don't care if Christopher Thorndyke is annoying, nor that this show's plot play exactly like the Sonic Adventure, Sonic Advance or any other Sonic game during the time the anime aired. The 4Kids version really messed the anime series up and made many people say "I like AoStH and SatAM a lot better than this crappy anime! Go drop it in a well!" The Japanese version is a lot better, because of the background music, better voice acting, and best of all, it's the original version of the anime.
The Sonic OVA shouldn't count. It's a movie, not an animated series. An animated series would consist a batch of episodes. Surely, it is two episodes long, but there's a reason they released in the US as a movie.
I would say that Sonic the Hedgehog Saturday Morning cartoon would be the best out of the four. Sure, it wasn't based on the games as much as it's weekday counterpart, but it did pretty well. A mix of lighthearted and serious without having it be qualified as 'kiddy.'
You don't need to tell us that the original Japanese version of Sonic X is better in Japanese, because almost EVERY anime's better in it's original language. Even so, it's still abysmal.