while I wasn't a huge fan of the singing, Tom Bombadil was a major tragedy to leave out when you understand why he was there. Tolkien explicitly wanted a character that left some mystery in the story, something unexplained, that couldn't be understood logically. Here is Tolkien's explanation of Bombadil from wikipedia
Tom Bombadil is not an important person—to the narrative. I suppose he has some importance as a 'comment.' I mean, I do not really write like that: he is just an invention (who first appeared in The Oxford Magazine about 1933), and he represents something that I feel important, though I would not be prepared to analyse the feeling precisely. I would not, however, have left him in, if he did not have some kind of function.
I might put it this way. The story is cast in terms of a good side, and a bad side, beauty against ruthless ugliness, tyranny against kingship, moderated freedom with consent against compulsion that has long lost any object save mere power, and so on; but both sides in some degree, conservative or destructive, want a measure of control. But if you have, as it were, taken 'a vow of poverty', renounced control, and take your delight in things for themselves without reference to yourself, watching, observing, and to some extent knowing, then the questions of the rights and wrongs of power and control might become utterly meaningless to you, and the means of power quite valueless...
It is a natural pacifist view, which always arises in the mind when there is a war ... the view of Rivendell seems to be that it is an excellent thing to have represented, but that there are in fact things with which it cannot cope; and upon which its existence nonetheless depends. Ultimately only the victory of the West will allow Bombadil to continue, or even to survive. Nothing would be left for him in the world of Sauron.[9]
And even in a mythical Age there must be some enigmas, as there always are. Tom Bombadil is one (intentionally).
So while not tragic to leave it out, it did leave out a part of the story that Tolkien found important, expressing the pacifist, and to me I just enjoyed that he was left unaffected by the ring.
Some of the quote sounds rather Jiddu Krishnamurthi-esque in their wording which is very interesting indeed.
For me, it was the singing that killed it... ;)
I liked how he was so happy. To be in such a state of mind all the day long. It is something I wish for myself, bit of inspiration. Even though I too found the singing to be, well, skippable without any consequences to the story.