Picking a Final Fantasy game will be too cliche for me, so I will go for another favourite series of mine, the old Phantasy Star games i.e. 1-4.
Phantasy Star was certainly great for it's time, especially being the only Sci-Fi based RPG when compared to Final Fantasy and Dragon Quest, which these would be considered the big three JRPG's from the late 1980's. Not to mention that Phantasy Star was also the first to be released outside of Japan.
Most people will always remember Aerith's death from Final Fantasy VII as like the most tragic thing ever in an RPG, but others also will remember Nei from Phantasy Star II, which predates FFVII by like 8 years.
I really wished Sega would produce a "Phantasy Star V" game as the original series is so missed and now overshadowed by these inferior hack'n slash type games.
Although Phantasy Star Online still remains one of the best online experiences I've ever had and showed what the good ol' dreamcast was capable off even with a crappy 56K dial-up modem, and Phantasy Star Universe, whilst silly in regards to it's story, some of the added and new improvements to the gameplay mechanics were actually good.
Another series that would be my favourite is Shenmue. Totally underrated and not many games these days still comes close to this in terms of detail.