In the Book:
At Crickhollow the Hobbits decide on a general plan of action for their coming travels. They sleep the night at Frodo’s new house, and rise early the next morning to begin the journey that will take them through the Old Forest. Though none of the hobbits are keen on going into it, the Forest presents the only route where they can get out of the Shire unnoticed. The dank, stifling, air, and the seeming watchfulness of the forest are disconcerting, to say the least, to the hobbits. Though the friends do their best to steer by the sun, the difficult terrain dictates their path and leads them not out of the forest but into its very heart. Heat and drowsiness- and perhaps something else- exhausts the hobbits, so that by early afternoon they are forced to rest for a time near a stream and an old Willow- this proves nearly fatal. The tree- the impression given is that this Old Man Willow is something of a dark Huorn – attempts to drown Frodo in the stream and traps Merry and Pippin beneath his roots. Sam, who was unharmed by the tree, hauls Frodo out of the water and the two then frantically try to free their young friends. In the nick of time, they encounter old Tom Bombadil.

In the movies: Omitted

Why the change?
Like so many other post-Hobbiton pre-Bree scenes, this sequence was in all likelihood cut from the movie for time constraints; it slows the story down and delays the more complex and vital action.