Eh? I don’t know about the other games you mentioned, but the Ultima series and FFX did not have your average story lines.
In the Ultima series (which are wonderful games, btw), you play a guy called The Avatar who has been apparently saving the world of Britannia since basically forever. You’re a normal guy in the modern real world. For example, in Ultima 9 you start out at your modern 2-story house circa the year 2000. When you’re needed in the alternate reality of Britannia, you get summoned and you start kicking bad guy butt.
I used to love that story mechanic! Heck, I still do!
In FFX, you’re not some humdrum villager, either. Since the story is so awesome (and the game positively cinematic) I’ll have to spoiler box this one:
[SPOILER] I mean, c’mon! You start out as a young star athlete in one of the biggest sports of the game world. You’re incredibly famous. That’s one thing that makes the protagonist not normal. The other thing? Oh, yeah… You’re not real. As you find out late, late in the game, you’re actually just a summoning. You’re a hero dreamed by the faye, which are the preserved dead spirits of your city that was obliterated a thousand years ago.
Not to mention the game starts out with your city being eaten by an enormous, anonymous monster. Only for you to wake up a thousand years in the future!
FFX had an incredible story. This spoiler is a bare taste of the depth that they couldn’t even explore in just one game. That’s another reason why FFX is the only FF with a direct sequel [/SPOILER]