Llaurentieu–I’m going to take a crack at this, because I am a huge LOTR fan, and have been all of my life. NOt only that, I have worked the dieties from that mythos in the past. I am guessing from your answer, Asbjorn, that you haven’t read the books (which is fine), but for those of us who love Middle Earth, the movies are absolute trash compared to JRR Tolkien’s writing. 
A little history: Tolkien wrote LOTR to give the Anglo-Saxons a mythology. Most of the Anglo-Saxon mythos has been lost. Unlike the Norse mythos, which has a lot of written record, there are only hints on the Anglo-Saxon belief systems. A perfect example is Eastre. She’s mentioned once by The Venerable Bede. That’s it. Everything else we have on her is conjecture. So, what historians can guess about Anglo-Saxon mythology has to be deduced by going back to German and Norse myths. So, what good ol’ JRR decided to do, was go back to create a plausible ‘proto’ mythology, that all of the Northern current (only he didn’t call it that, because they didn’t use words like that back then, plus he wasn’t a sorcerer) might have derived from. Of course, JRR was also a staunch Catholic, so you definitely see how that influenced his myths. Tolkien was not only inspired by the Germanic myths, he actively went back to try and unify them to give his people (The English) a series of myths that belonged to them, separate from the Germans (remember, he fought in WWI, the Germans were not his friends). He was professor of linguistics, with the Germanic languages being his specialty, so he knew his stuff.
I will have disagree wholeheartedly with Asbjorn on the accuracy–I think that Tolkien’s redition of the beings in LOTR is acutely accurate with those beings that they are derived from in the Northern Current. The movie, for those who have not read the books, does a really rotten job of portraying the people and races in the books accurately. In the three novels that make up the trilogy, the elves are alfar all the way, the dwarves are as svartalfar as you can get, the ents are landvaettir, and the hobbits are hausalf/brownies/kobolds/etc. If you’d like me to go into more detail, please let me know, because I write an entire book about each of these races and how they correspond to the Norse mythos/current.
But–let us go to the crown jewel of Tolkien’s mythology–The Ainundale. I fell in love with this book the first time I read it. What Tolkien tried to do with this work, was take the Germanic gods and boil them down to their essence, where they might have ‘come’ from. Obviously it is not historically accurate, and one can definitely see a lot of Christianity thrown in. (But then, there are agruments about whether Lif and Lifrarthisir are Christianized additions to the Norse myths or not. So, one could historically argue that that there is less Christianization than we think, or that there is more.) It is historically accepted that Freya, who only occurs in Norse Mythology, and not the rest of the Germanic children of the original mythos, is a fracture from Frigge. In fact, her name in Anglo Saxon is is pronounced Free-ya. Freya, itself, is the colloquial word for lady…so it could very well be that Frigge was referred to a Freya Frigge (Lady Frigg). Tolkien tried to go back and put all these splinters back together.
So, a possible thought process would be something like: Odhinn, Woden, Wotan, Godan were the ‘same’ god (though not really, they’re all a little different). Who was the dude who was the original? What was he like? So he looked through all the myths about this guy, and put together what might have been what the orignal guy was like. Now, one aspect of Odin which is present in all Germanic myths is ‘The Wanderer’. This is one way that he presents himself to human beings on Midgard (which translates literally as Middle Garden, or Middle Earth, because we’re in the middle of the world tree, and all other worlds flow to us). In his mythos, all of the ‘other’ words also flowed to Middle Earth. It was the place to be. 
But I digress. So, this wandering aspect of Odin was present in all renditions of his myths, so Tolkien surmised that was part of the original aspect of this diety. For that aspect, he created Gandalf for his story.
Now, for those who have read LOTR, we know that Gandalf is not the fluffy bunny that the movies make him (yes, compared to the books, that wizard is a softy). For those who have read The Silmarillion, we know that Gandalf, when he wasn’t just in his guise of the Grey Pilgrim, kicked ethereal ass. I would discribe the Gandalf we see in the books, as “The Elf from the North” (which is what his name translates as), as an Odinic current, a little current within the Norse current. He is Vegtam the Wanderer, as opposed to Odin The All-Father. Gandalf is very much Vegtam with a different name.
I’ll stop here, because I would, honestly, go on for pages, and I know this is probably way more than you asked for!