My images of most of the characters were fairly well-defined before Jackson's movies came out and, in the long run, I don't think they were much affected by them. I say 'in the long run' because as I think back, it seems to me that in the immediate aftermath of those films, I did tend to picture the characters a bit more like those in the movies; but I think that now those images have largely reverted to what they were before.
On the other hand, I think the Bakshi animated movie (which I saw when I was rather young and not long after first reading the books)
did influence my images of some of the characters quite a bit. I tend to picture the hobbits, with the exception of Sam, rather as they were in the Bakshi film. Boromir too (though without the infamous viking helmet). My image of Gimli tends to be close to the Bakshi version as well, though John Rhys-Davies isn't that far off either (except for the accent).
Cate Blanchett's Galadriel is very much the way I imagine her, though I think this is more an instance of Jackson hitting the nail on the head than of my image of her being influenced by the films. In any case, I never found her portrayal by Bakshi particularly convincing. Eowyn is another case where my mental image is very close to Jackson's version, and in this case it may well be due to the influence of the films.
There are a few characters of whom I have fairly definite mental pictures that are not at all like either the Bakshi or the Jackson version. Sam, for example. I never pictured him as particularly fat - perhaps a little on the stout side when the journey begins (actually I imagine Frodo to be a little stout at the outset as well). And neither Sean Astin's somewhat featureless face nor the near-caricature in the animated version is quite right if you ask me. Aragorn, too, in my mind looks nothing like either the animated version or like Viggo Mortensen.
Now that I think about it, another strong influence on the way I picture the characters is from various illustrators, particularly the Hildebrandt brothers. Bilbo, for example, looks rather like
this for me, though without the glasses. The Dwarves in the
The Hobbit I picture more or less like
this. And while much of the Fellowship in
this picture looks completely wrong, I think it may be the source for my image of Sam.