Good question.
(Not counting compilations like Sonic Gems or MegaMan X Collection)
Sonic the Hedgehog: 1, 2, 3, Sonic & Knuckles, Spinball, Sonic Adventure, Sonic Adventure 2, Sonic Shuffle, Sonic Heroes, and Sonic and the Secret Rings. That makes ten.
Final Fantasy: VII, VIII, and IX, followed by FFT for PS1 as well as War of the Lions for PSP. That makes five.
Dynasty Warriors: Empires 4 and Empires 5. That makes only two unless I count Samurai Warriors, SW: Extreme Legends, and Samurai Warriors for PSP. That would make five, even six if I threw in Crimson Sea 2 as salient.
Overall, I usually don't stick with a series past the second mark. I guess I kind of feel like, "if they can't get it right by the first sequel, they're never going to." On the other hand, there are games like Kingdom Hearts, which I adore, but will not buy any of the sequels for simply because I found absolutely nothing wrong with the first game, nor anything that would make me want to sully that experience by trying out a potentially disappointing sequel (which, from what I've seen, is more or less the case).
Games I wish I had more of (series-wise): Ys, Phantasy Star, Kagero (Trapt), and Legend of the Heroes.