When I try to fit him into US mythos, I think of Paul Bunyan or Bigfoot--because of the physical, naturally. But Bunyan accomplished something--his legend had a simple lesson, and Bigfoot of course has none that I can think of, except to be exotic and mysterious.
I can't think of a place in US lit where he would fit, can you? This may be only my own inability to separate him from the story in which I encountered him, so I'd be interested to see where you can place him.
Honestly, the guy that leapt to mind? Jim in Huck Finn. Which sort of emphasizes ita's point.
Any faithful retainer that needs to be rescued by those he works for, really. I can't think of any white ones right now, and I don't want to muddy the waters -- I don't mean magical.
I don't see what's Bunyanesque about him at all, honestly.
Personally, I think that Hagrid kinda-sorta fits into the mold of several of Dickens' supporting characters. Good-hearted, mildly eccentric, a little doltish, not quite fitting with polite society, good for comic relief, and so on. There are quite a few Dickens characters who remind me of Hagrid in one way or another--Mr. Boffin, Polly Toodle, Joe Gargery, Captain Cuttle, and so on.
I think that Hagrid kinda-sorta fits into the mold of several of Dickens' supporting characters.
In an exclusively British way, though?
No, not exclusively British, since that kind of character also appears in Twain (Jim, as was noted). Maybe it's not that Hagrid is particularly British but that he's rooted in the 19th century.
Barkis came to my mind. He needs young David Copperfield to do his courting for him. English, though.
This may be a stretch, but what about Klinger in MASH? He isn't very good at his job, he's eccentric, he doesn't fit in, he's less educated than the people around him, and the "good" people accept him as he is.
Yeah...except now I've got Hagrid in a dress running around in my brain, and well, I wish I didn't.
Great, now I've got him in that little Eleanor Roosevelt hat that Klinger always wore....