I have my problems with Peter Jackson, but on this decision he made the right call.  Not because Tom Bombadil is a bad character, but because in the medium PJ was working in, he no longer serves the same purpose.

For my videos on some of the issues raised here regarding Bombadil and the slow progression of danger as Frodo leaves the Shire, check the following:

The Old Forest: https://www.youtube.com/watch?v=Y1ODkwQ-lnY

In the House of Tom Bombadil: https://www.youtube.com/watch?v=IKfG0vP_INs

Fog on the Barrow Downs: https://www.youtube.com/watch?v=JmY2ah1s2yo

The significance of these three chapters: https://www.youtube.com/watch?v=BIu8TAYBu7E

Frodo leaving the Shire: https://www.youtube.com/watch?v=-jTXY8I5wAY

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