Okami. Naturally, this will be limited to a very short run, probably 13-26 episodes, including secondary content (read: side quests) and maybe a couple eps that feature original material. What we WOULD get, however, would almost certainly be magnificent. Throw in some action sequences at the right moments, have Ammy go full-tilt Okami Amaterasu on a big bad, and I'll be humping air.
Sonic. Yes, I know, there have been 3 series so far (not counting OVAs and such) but it's high time for another one. I honestly rather liked the (slightly) expanded universe that came about from Sonic Adventure and Sonic Adventure 2. Unfortunately, Sonic X, while not the worst cartoon, doesn't quite do it justice. No, what I propose is something like this: The characterization of Sonic Adventure (2) mashed up with the gravitas of Sonic the Hedgehog (the "good" cartoon show). Something like that. Honestly, the idea is only half-formed in my head, but what I'm imagining is pretty damn cool.
Final Fantasy. Just about any of them would work. Actually, the first one might work best simply because there's so much room to expand. More importantly, one could take this as an opportunity to defy character archetypes. For example, give the black mage a quest to redeem the good name and dignity of black mages everywhere. Instead of an all-forgiving compassionate white mage, said white mage refuses to heal anybody deemed wicked, based on some kind of tragic past.
Asura's Wrath. If you're not familiar with Asura's Wrath, I know there are a few articles on the Escapist that will explain why it's not your average game. Indeed, I hesitated for a moment in calling Asura's Wrath a game to begin with. While it works fine as a game, there's not much doubt to that, there's so much dialogue, plot and characterization that happens outside the gameplay. In other words, I can't help feeling that the narrative has been shunted to the side in favor of watching Asura go ballistic for the 36th time. With a proper anime, we get a nice compromise, and IMO, a better experience overall.