Focusing on the main series and ignore spinoff games (including sequels)...

JRPG in which you take control of a character and guide them through their story, generally involving the saving of the world in some manner. An innovative series, each game showcases new features/systems as opposed to just re-using existing systems. Each game is also set in it's own world. As for the MO, it would involve chocobos, crystals, fantasy races, fantasy worlds. Like with everything else in the series, the technology also sees consistent change between traditional fantasy, steampunk and science-fiction, although it should be noted that magic exists in all worlds, and melee weapons are utilized in every game. All battle systems are turn-based to some extent, with more recent games using time and action speed to dictate turns.

I don't think many feel the series is getting better and better. I do think some feel it is getting worse. I feel the majority simply like different games in the series, and the chronology of release matters little in their minds when establishing such things.