In some ways it doesn't seem that long ago, in others (where it connects to very early memories of the books) it seems like it's always been there.
It's why I don't generally run or play standard fantasy - I know I can't GM like Tolkien can. I'd love to have a hand in something like that, but so much standard fantasy is just about fighting through Moria rather than grieving over Gandalf, getting up the mountains rather than the importance of fellowship.
The One Ring goes towards building this in, but I think it might make it too planned out. Really, you need a group who can throw themselves into it.