Most memorable NPCs outside of main scenario or sidequests?

[Rocl]

Actually she doesn't remember all 1.0 players, only those who specifically had the Legacy storyline (that is, they completed the Lunar Transmitter battle in 1.0 and is therefore designated as one of the 'original' Warriors of Light) - she treats any other 1.0 player exactly the same as a new adventurer just newly woken to the Echo. I know this for a fact as she didn't respond in any different way to my character who I transferred from 1.0 (and which I never did the 7th Umbral Era story for, thus I did not get the Legacy storyline in ARR), she just acted like she had never seen Enki before.

Either way, it seems in Minfilia's case it wasn't that the Echo 'protected' her from the amnesia, more she used the Echo to view that character's memories and saw who they were. But again because I didn't get the Legacy storyline in ARR I'm not certain of exactly what it is she said to a player who had the Legacy storyline, instead having to rely on secondhand info, so take that with a grain of salt.

Ah, this I can tell you. When remeeting Minfilia at the Waking Sands again, she pulls you aside and tells you that the rest of the Scions (and most of the world) has forgotten you. She doesn't know why, but she asks you not to say anything. (Tataru mentions you seeming familiar, but I'm not sure if that's Legacy dialogue off the top of my head. Though she does find your name in her logbook? She doesn't fuss about that at all though, and it could be her writing it down)

Minfilia, Scions of the Seventh Dawn MSQ:

After five long years...you've come back to us, just as Louisoix said you would...
Words cannot describe the joy I feel at this moment. Welcome home.
Aye, I remember you still, and everything you fought for. Know that you are not entirely forgotten.
If Louisoix is watching us, as I choose to believe, he may now rest in peace, his mission finally fulfilled.

Minfilia, A Wild Rose by Any Other Name MSQ:

Forgive me for treating you as a stranger. I know you deserve better than this, considering all you've done for the realm.
It remains unclear why no one remembers you. We can only assume that it is a consequence of the power that Louisoix invoked to save your life.
But irrespective of the cause, know that whatever shroud has fallen upon people's memories, there will surely be a way to lift it.
Thank you for understanding.

Cid, Lady of the Vortex MSQ:

Cid: It took a while for the memory to return, but I remember you.
Cid: The floating isle, van Darnus... We ended it, that day─or so we thought.
Cid: Listen─let's keep this between the two of us, for the time being.
Cid: If word got out that one of the Warriors of Light had returned, the eyes of the world would soon be upon us─our enemies' included. And that's the kind of attention we could well do without.
Cid: What, isn't it enough that I know the truth?
Cid: Don't worry. A man of your talents won't go unnoticed for long. Someday, they will remember you─and you'll never know another moment's peace!
Cid: There, up ahead! Ready, old friend?
Cid: Hah! Some things never change! We're going in!

In this case, I'd said us using the Echo to help him unlock his memories pierced the shroud of amnesia as well.

There isn't much other dialogue I can recall until The Ultimate Weapon MSQ:

Minfilia: Please, Mother Hydaelyn. Please light his way through the darkness...
<flash of light, blue streak across the sky>
Y'shtola: It's him. I feel his presence!
<flash of light, blue streak across the sky>
Yda: Can it be─? Is it really him!?
Papalymo: I knew it! I knew it all along!
<flash of light, blue streak across the sky>
Kan-E-Senna: Who speaks...? The Crystal! She calls to us!
Merlwyb: I hear Her! The voice of Hydaelyn Herself...
Raubahn: She speaks of...
Strike me down! No wonder he seemed familiar! he's one of the Warriors of Light!
Raubahn: What are you smirking at, Cid!? You knew, didn't you!?
Cid: Oh, you mean our adventurer friend? Did I forget to mention he was one of the Warriors of Light?
Cid: Saved Eorzea, you know. Twice.
<Minfilia cries>
Minfilia: The shroud is lifted. They remember you...

I don't recall much other Legacy text in the MSQ, but I'm quite sure there's some sprinkled throughout. The next big thing I recall is Alisaie knowing you slew Nael van Darnus and Nael Deus Darnus knowing you killed the mortal vessel at Rivenroad as well. Given Deus Darnus' ambiguous status as "aetherial shade / simulacrum" we might be best to assume immunity to memory warping techniques. (I would say as a consequence of being Tempered, we know one with the Echo can't be Tempered, so one Tempered shouldn't be able to receive the Echo.)

After Final Coil Urianger does offer a theory for why the world forgot you:

Urianger: And though the veil hath been lifted from many and more mysteries, the haze which shroudeth the people's memory of the Calamity yet eludeth explanation. I have but half-formed theories, which I would share with thee, if thou art willing to listen.
Urianger: As thou knowest full well, when the combined might of the Twelve failed to contain Bahamut, Master Louisoix mustered what strength remained to him and sent you and yours beyond the reach of space and time.
Urianger: From his final words to the Antecedent, I doubt not but that he intended this from the first.
Urianger: 'Tis my belief that he invoked the power of the Keeper, and sent thee to a place outside of time, beyond the reach of the primal's wrath. Taken whence thou rightly existed, thou didst leave behind a rent in the fabric of reality.
Urianger: At the selfsame juncture, Master Louisoix struck down Bahamut, thus triggering the realm's dramatic regeneration. The occurrence of these events in rapid succession, I theorize, gave rise to the people's clouded recollection of the Calamity.
Urianger: Five years from that fateful day, thou didst return to us, to once again become Eorzea's valiant blade. Though my beloved master is gone, his hopes and dreams live on within thee, Warrior of Light.

That said, he doesn't offer up why some people remembered you. I'm unsure of what "half-Legacies" like Enkidoh experienced, as a consequence of only getting the "full-Legacy" experience (I'm not really sure how to differentiate the two, sorry). Was there the benefit of the altered opening (teleporting in at Snakemolt, the stone of Althyk's new location) or just the mostly out of character bonuses? (Reduced sub fee, goobbue mount, dated items, tattoo, etc.) I suppose if it's the latter, it might be safe to assume even though the character simply didn't canonically develop the Echo until after the Seventh Umbral Era. A bit boring and lame, but as with most things in an MMORPG story regarding your player character, something easy to fudge for your own headcanon/RP purposes. If Louisoix did teleport you away as well, then I've got nothing.

I do feel it important to point out it's doubtful Minfilia used the Echo on you, as she specifically bemoans not being able to control the Echo in the very quest you're introduced to her.

In short, the Echo is a truly extraordinary power. And this power is strong within you.
It is only a shame that we cannot use it whensoever we choose.
That's right. I too possess the Echo.

(She explains this to you even if you're Legacy, and in 1.0 you definitely had "Use the power of the Echo?" prompts which seemed an awful lot like choosing when to use it but I digress.)

If it wasn't for Rostnsthal, Warburton, and some others I'm likely forgetting, I would write off all the "original 1.0" storyline as non-canonical/retconned. (That is, anything pre-Yoshida/7UE) It just seems that should you not be a Legacy player, these events still happened just without a meddling time-hopping greenhorn adventurer.

The next big thing is the curtain of amnesia over Hydaelyn's citizens lifted all at once? I'm not sure, I think I recall other minor NPC dialogue changing, but I have nothing concrete. F'hlaminn, I don't think, has any extra dialogue should you have been an Ul'dahn Legacy player, for example. How did Alisaie (and Alphinaud, who furnishes her with the information) know that you slew Nael van Darnus? Was it some record kept in a book somewhere? Did Alphinaud know who you were the whole time? I don't think we have answers for this.

Likewise, I can't think of another Echo-blessed character we've met in both 1.0 through 3.0 so far other than Minfilia. I don't think it's a stretch to assume the Echo was somehow involved in her memory preservation though. I think Una Tayuun might've been the Echo user in her party, but she suffers from some degree of memory loss as well. She has a strong inclination she was a Scion, but they weren't called Scions back then.

Why don't any o' these blokes know who I am!? I swear I was one o' 'em Scions o' the Seventh Dawn!
Only we didn't have such a fancy name back then, an' the headquarters was in a far more convenient location.
At least, I think it was... Or is me mind playin' tricks on me? Gods, what's wrong with me? Why can't I remember it more clearly?

I can't recall which of those lines is "Legacy" only, if any are. But in the five year time skip she also appears to have developed quite the accent as well. The other two, best I can recall, you can't even interact with. Speaking of hazy memories, I swore she had a bit of dialogue about Tataru finding her names in the Logs but I can't find it flipping through these notes and files and tables...