I've only played most of the first one so far. :'( But, I'd say my favourite case would have been 'Turnabout Sisters'.
*thinks through all four games*
Uh... I suppose it's mission 4 in Gyakuten Saiban 3, I've played it like 5 times over.
Rise from the Ashes.
Damon Gant is awesome. And he's darn hard to convict.
I'm on 3-3 right now.
2-4 has one of the best stories of any game I've ever played. I would have bought the game just for that if I had known how awesome it would be.