Shenmue is, no joke, the father of modern gaming. Just about everything you can think of that is common in AAA games today, was pioneered in Shenmue. Even little things you wouldn't expect, like procedural generating forests, stems from Shenmue. When Shenmue was in production, it was something that was literally 15 years too early. Insanely ground breaking.
In terms of gameplay, it's a mix of an adventure game kinda like Heavy Rain, albeit more open, and an action RPG, with the combat itself being lifted from Virtua Fighter. You train, you level up, you learn new moves. In Shenmue I, the focus is on day to day living, perhaps more like harvest moon or any other daily sim game, but shenmue II is much more of a story focused game, with a much bigger emphasis on underground fighting tournaments. There isn't much combat in shenmue I, where shenmue II is full of it.
Unfortunately, the format shift between shenmue I and shenmue II ruined some of the more ambitious aspects. Example, even though there isn't much fighting in Shenmue I, there is a dojo where you can train and level up, and the game highly encourages it. THis is because, when you get to shenmue II, the moves you learned carried over, so you'd have a custom-made fighter for Shenmue II that would affect your approach to the underground fighting tournaments. But since Shenmue I was on the dreamcast, and shenmue II in the us was on the xbox, they couldn't transfer saves, and thus they just basically gave you all the moves in the US version of shenmue II, ruining the character-building.
The story itself is classic wuxia kung fu. It begins grounded with a mystery -- you come home and see your father murdered before your eyes by a chinese man named Lan Di. Your father, who was a martial arts master, hands of a sacred mirror to Lan Di before Lan Di performs a forbidden and fatal technique on your father. In his last dying moments, he begs you to keep your friends close. Ryo vows in that moment to avenge his father's death.
Pretty much all of Shenmue I is focused on beginning your adventure, i.e. raising money to travel to china to begin your quest. As such, it's kinda light on story. You discover that the mirror your father handed over was part of a pair, and that he had hidden the other mirror on the grounds of his dojo which Ryo finds. These mirrors are ancient magics, and it's said whoever holds both of them can summon a dragon that will devour the world.
Shenmue II is where everything really kicks into high gear. Ryo travels to china and finds out more about Lan Di, the mirror, and his own destiny. Throughout Shenmue I and II there is a repeated legend that is narrated:
He shall appear from a far eastern land across the sea,
A young man who has yet to know his potential,
This potential is a power that could either destroy him or realize his will,
His courage shall determine his fate,
The path he must traverse, fraught with adversity, I await whilst praying,
For this destiny predetermined since ancient times,
A pitch black night unfolds with the morning star as its only light,
And thus the saga… Begins…
You uncover that your father and Lan Di had a shared past, that there is a secret society of martial arts masters who are trying to gather the mirrors, and that there is a young woman living in the mountains that Ryo has been destined to meet for hundreds of years. This young woman seemingly has otherworldly powers and can communicate with nature in strange, unknown ways. In their brief time together, Ryo sees her do a number of pretty weird, mystical things.
Along the way, you also go through a surprisingly star-wars like adventure. You meet Ren of Heavens, for example -- probably the closest Shenmue has to a Han Solo. You fight crime lords. You travel to the ancient walled city of Kowloon. It's great. Shenmue II ends with a massive, massive cliff hanger, just as the story reaches it's climax. That's why people have been dying for it.
The other side of why this is such a requested series is because of YU SUZUKI. This is his magnum opus. His life's work. Yu Suzuki is Mr. Sega. Think of a classic sega game that ISN'T Sonic or Shinobi, and Yu Suzuki was involved. Yu Suzuki was the heart and soul of Sega's arcade empire. Hang On, Space Harrier, Outrun, Virtua Racing, Virtua Fighter, Daytona USA, etc -- all Yu Suzuki. Shenmue was basically the last thing he was ever allowed to work on. When the Dreamcast died, Sega's best developer was given a "window seat" where he was technically still an employee, but not allowed to make anything. For 20 years, he was on the "window seat." Imagine if Shigeru Miyamoto disappeared after Mario 64 and wasn't allowed to make games. THat's what happened with Yu Suzuki.
Shenmue III is Yu Suzuki's grand return to gaming. And Shenmue III is being made by a restored version of AM2, his classic team.
The hype for Shenmue III is real.