It is specifically stated in Fellowship that Old Tom couldn't have taken the Ring. Though it had no power over him on his on land (the Old Forest, to those allergic to reading), Sauron's lot would have destroyed Middle-earth eventually anyway, and ultimately Sauron himself would have come to the Forest to take the Ring. Tom couldn't have come to aid the war beause his power only lasted withing his borders, and he wouldn't have cared until it had begun to affect him and his trees anyway.
Watching the extended editions of Fellowship and the Towers, it seems that Tom is the only major element left out. And if you watch the extended Towers, you'll see Treebeard trot out
of the phrases from the missing Bombadil chapters.
Seems to me that in his book, Tolkien would add the characters that he wanted sometimes for the sake of it - Tom and Treebeard were always going to be in LOTR, even from the first vague plans. When Faramir 'turned up', Tolkien had intended to drop him but found that he liked him too much. Film makers like Jackson simply can't afford to work the same way.
None of this excuses the cliff scene though, which I will hold against Jackson for the rest of my life.
