Here's a list of some of my series I've been fortunate to come across throughout the years.
Starting all the way back on the PS1, this series is games is very story driven. Granted, they all start to blend (unlikely heroes save the world), but they are unique enough if you like a good story.
How many times does the world need to be saved? Until Japan decides we're done, I suppose. Fun series, with the exception of a few (X-2, 13 in particular). FF7 got me started on my journey.
Games are far better than the movies (fight you all day on that) - starting on the PS1 with Harry looking for his daughter Cheryl, while combatting monsters, yourself & the town; it's a cult classic.
Simple game, 2.5 D world, 2 D fighting, with an odd element of dating sim that didn't have any clear benefit to gameplay; relatively short, but worth a playthrough.
Aya Brea fights monsters created by the powerhouse of the cell in 3 different games (2 on PS1, 3rd on PSP). Controls & camera like Resident Evil & Silent Hill.
Pseudo MMORPG, original games came with a DVD series. Trying to figure out why people playing a game are falling into comas after being attacked by an unknown enemy.
Remake of the GU series on the PS4 contained only that series, none of the original, as of yet.