Here's a quote from the end of the Hobbit that Viv posted on her blog:

'Then the prophesies of the old songs have turned out to be true, after a fashion!' said Bilbo.
'Of course!' said Gandalf. 'And why should not they prove true? Surely you don't disbelieve the prophesies just because you had a hand in bringing them about yourself? You don't really suppose, do you, that all your adventures and escapes were managed by mere luck, just for your sole benefit? You are a very fine person, Mr. Baggins, and I am very fond of you; but you are only quite a little fellow in a wide world after all!'
'Thank goodness!' said Bilbo laughing.