Well, I'm not a "mythicist", which is to say that I don't believe that Robin Hood is a watered-down version of Celtic, Saxon or Germanic God.
I do believe that there are some mythic elements in the legend, and some show up quite early. But I don't think it is directly the genesis of the legend.
The main reason for this is that in the early Robin Hood ballads, what seems mythic is largely subtext and interpretative. It's very easy to see the fight between Robin and Guy as a winter vs. summer conflict, and it did like stem from a performance like the 1475 dramatic fragment. There are some vague mythic touches around Robin's death. But to take 1 percent of the stories and say that's the dominant element strikes me as a bit deceptive.
And it's nothing like what we get for stories like those of Eustace the Monk, where he's actually using overt magic. And the thing is -- Eustace was a real guy. His existence is not nearly as murky and disputed as Robin's. So, I have to wonder why Robin's early legend isn't as mythic as the stories of Hereward, Eustace or Fulk Fitz Warrin - people who actually lived but had grand deeds ascribed to them.
I think a lot of the mythic elements in the Robin Hood legend seem to come from his role in the May Games. Now, I don't want to undersell the importance of these games. Since we have more references to these festivals than all other English folk drama of the period (15th and 16th century) combined, well one could say that the Robin Hood of the May Games was THE Robin Hood. But the mythic aspects here predated Robin's involvement in the games. It feels like something that the legend probably acquired here.
Gillian Edwards noted the similiarities between Robin Hood and Robin Goodfellow. Suggesting that the name Goodfellow can also mean thief or boon companion, both adapt descriptions of Robin Hood. And both characters are known for misleading travellers. While "Robin" has some mythic associations in the middle ages, the first instance I could find to the name "Robin Goodfellow" was after the first appearances of the Robin Hood ballads. It makes me wonder if perhaps Mr. Goodfellow is a mythologized version of Robin Hood, rather than the other way around.
The 19th century seems like the big period for the mythic Robin Hood. That's when you start to get pantomimes where he wanders into fairyland or fights characters like "the Gnome demon". And a few children's books use these elements.
It's also when historians really start to view Robin Hood as a folkloric figure, a god or sprite given flesh. Some of these arguments are based on misunderstandings of the Robin Hood legend. One famously argued that Robin was a coven leader because there were always 12 men in the Merry Men. Nice -- except there weren't always twelve. The ballad of Robin Hood and the Monk has Robin being told to take 12 of his best men, which implies he has more. In A Gest of Robin Hode, there are 140 members of the band. And it seems to vary elsewhere. (John Matthews is better informed about the Robin Hood legend, but his own book on the subject contains numerous errors.)
Stephanie Barczewski has argued that the folkloric associations given to Robin in the 19th century might have something to do with Anglo-Saxon "racialism" of the period. Essentially doing for England what Wagner did for Germany. And if some of those Saxons vs. Normans Robin Hood stories give me the wiggins, some being a little too keen on praising the purity of the Saxon race.
I think the biggest promoter of a mythic Robin Hood now was actually a TV show, Robin of Sherwood. And a very good TV show it was, one that film producers and novel writers continually rip off without giving appropriate credit. In that series, Robin is the servant of Herne the Hunter, a personification of the Horned God.
There have been a few other occasions previously where the Horned God legend has intersected with Robins. But not as many as you'd think. It's such a natural fit, that I know many people who assumed that this connection predated the TV series. And yet, the show's creator, Richard Carpenter, has said he was just looking for a Merlin or Obi-Wan Kenobi figure because fantasy seemed popular at the time.
And yet, this TV show has let many to Paganism. Which again, suggests what a good fit the concepts can be.
But they don't have to fit together. Think of all the Robin Hood stories with no magic.
So, where does that leave me? Well, feeling that the legend's origins probably have more to do with real world outlaws, but not completely dismissing the mythic side either.
For an argument from the "mythic" perspective, I suggest people check out: http://hesternic.tripod.com/robinhood.htm
I don't always agree with Hester, but she knows the legend far better than most mythicists who have published on the subject.
In the end, Robin remains a subject for interpretation. Hard to pin down. And viewed different ways by different people.
And I suppose that's what bugs me when I get email complaining about the right-wing Christian movements supressing the truth of the legend. And that anyone who doesn't think Robin Hood is Pagan god made flesh is some evil, anti-Pagan. And yes, I have got those kinds of emails -- and just as dogmatic ones from people who think Robin Hood was based off solely a real person (in some cases, the supposed ancestor of the person writing me.) These emails suggest that there's one right way of looking at things, and I don't believe there is.
Oh, and then there's the Kirklees vampire story. But well... no need to go there.