I haven't read the books and I don't even know if he is a character in the books, I assume he is, so I'm curious to know if he says anything apart form that one word? He only seems to say that in the TV version.
No, in the books this is the only word he says. Interestingly, Old Nan points out that Hodor is not even his real name:
Theon Greyjoy had once commented that Hodor did not know much, but no one could doubt that he knew his name. Old Nan had cackled like a hen when Bran told her that, and confessed that Hodor’s real name was Walder. No one knew where ‘Hodor’ had come from, she said, but when he started saying it, they started calling him by it. It was the only word he had.
Even when Bran possesses his body to fight the wrights outside of the three-eyed crow's cave. He screams with rage as he fights with Hodor's body and something like "HODOR HODOR HODORRRRR!!" is what comes out. Bran doesn't want them to know of this ability so he doesn't attempt to talk outside of a "Hodor" here and there to convince the others that nothing is amiss. I suspect that even if he did though he wouldn't be able to, much like trying to speak as a wolf.
He has only ever said Hodor in the books and Bran even comments on this at least once.
Yet now that the last day was at hand, suddenly Bran felt lost. Winterfell had been the only home he had ever known. His father had told him that he ought to say his farewells today, and he had tried. After the hunt had ridden out, he wandered through the castle with his wolf at his side, intending to visit the ones who would be left behind, Old Nan and Gage the cook, Mikken in his smithy, Hodor the stableboy who smiled so much and took care of his pony and never said anything but "Hodor," the man in the glass gardens who gave him a blackberry when he came to visit …
A Game of Thrones, Bran II
Apparently he does hum at least once too, though not another word it is another sound he can make.
They left Old Nan in the tower room with her needles and her memories. Hodor hummed tunelessly as he carried Bran down the steps and through the gallery, with Maester Luwin following behind, hurrying to keep up with the stableboy's long strides.
A Game of Thrones, Bran IV
Though he wasn't always called Hodor, but once Walder, or Wylis in the show.
Hodor lifted Bran as easy as if he were a bale of hay, and cradled him against his massive chest. He always smelled faintly of horses, but it was not a bad smell. His arms were thick with muscle and matted with brown hair. "Hodor," he said again. Theon Greyjoy had once commented that Hodor did not know much, but no one could doubt that he knew his name. Old Nan had cackled like a hen when Bran told her that, and confessed that Hodor's real name was Walder. No one knew where "Hodor" had come from, she said, but** when he started saying it, they started calling him by it. It was the only word he had.**
A Game of Thrones, Bran IV
In the show it has been revealed how Hodor got his name, via seeing his future self holding a door whilst being clawed by wights as Meera Reed told him to "Hold the Door" repeatedly.
The meaning behind the name is the same as the books but apparently it will come about in a different context. Though the quote is from reddit I've read the same thing before from "something official" but can't find it now.
Someone asked him about the show's Hodor name reveal. He said that his name reveal in the books will differ in the context and how it happens. So while the name will still mean the same thing (Hold the Door), it will be very different from the show's reveal. He said he came up with the name idea in 1991 and seemed depressed that the show got to reveal it before he did.
r/asoiaf, Got to hear GRRM's thoughts on a name reveal tonight
As such we can speculate he said more than just Hodor before his life changing event and he's probably also said "Hold the Door" a few times, but again this is all before he became known as Hodor.
I truly think I have the discovered the "real" reason and it simply has to do with the character that he is base upon "Loial" from the Wheel of Time series. There comes a time in the series where Loial tells "Perrin" that he will guard a door with his life if need be beyond which "Faile" lies unconscious. Perrin is the character who Bran is based upon and Faile is the character who Meera is based upon. Loial is an Ogier who is a giant compared to men. Perrin has a strong attraction to Faile at this point in the story the same as Bran towards Meera. The differences. Where Loial is a bookworm and very intelligent; Hodor appears to be a simpleton on the surface. Faile lies unconscious in TWOT where it will be Bran in ASOIAF. If you substitute "Guard the Door" for "Hold the Door" you get "HODOR". Bran wargs Hodor to Hold the door to protect Meera and that is his only thought. Bran's only thought at that Moment to protect the girl that he loves gets transported back in time to the young Hodor due to Bran's ability to time jump and sort of leaves the seemly intelligent Hodor with a form of PTSD allowing him to only say the words "HODOR" from that moment on.