Even though Parasite Eve comes as a close second, Lufia II is pretty much the epitome of gaming (and RPG's) to me 
As for the reasons why, it's because to me, it had the best overall package in any game i've ever played. Sure, some other games have done some individual aspects better than Lufia II, but in the overall panorama, no other has pulled all aspects together in such an epic way.
It had some of the best set of characters ever created. Maxim, Selan, Dekar, Guy (these two especially are pretty awesome, their antics are hilarious), Artea, Lexis and Tia
It had some of the best villains (if you could call them that) ever in a video game. Even though in the surface they look like your old run-of-the-mill destroy the world villains, they have a much deeper purpose. The Sinistrals are an order to be respected, not by fear, but by comprehension.
It had one of the best world stories ever created, and you really need to play Lufia II to understand the whole stance on the universe as why the Sinistrals are needed as a balancing force.
And it had the best puzzle and hardest puzzle ever created for a video game. Heck even the title given inside the game hints to that "The World Hardest Puzzle" 
It really is. Even with a faq and a youtube video on how to do it, you'll screw up the first, the second, the third, the fourth and possibly the fifth time 
Imagine doing it without any help back in those days
Current PC Build
CPU - i7 8700K 3.7 GHz (4.7 GHz turbo) 6 cores OC'd to 5.2 GHz with Watercooling (Hydro Series H110i) | MB - Gigabyte Z370 HD3P ATX | Gigabyte GTX 1080ti Gaming OC BLACK 11G (1657 MHz Boost Core / 11010 MHz Memory) | RAM - Corsair DIMM 32GB DDR4, 2400 MHz | PSU - Corsair CX650M (80+ Bronze) 650W | Audio - Asus Essence STX II 7.1 | Monitor - Samsung U28E590D 4K UHD, Freesync, 1 ms, 60 Hz, 28"
