Well there are lots of possible answers to this question but I guess the biggest thing he lost as the tale comes to its conclusion is his respectability. When he returns to his Hobbit hole, he finds out that his relatives have presumed that he is dead and are in the middle of auctioning off his property. Although he does get the majority of his possessions back (having to buy most of it) he discovers that his public standing appears to have changed irrevocably.
Indeed Bilbo found he had lost more than spoons - he had lost his reputation. It is true that for ever after he remained an elf-friend, and had the honour of dwarves, wizards, and all such folk as ever passed that way; but he was no longer respectable. He was in fact held by all the hobbits of the neighbourhood to be "queer" - except by the nephews and nieces on the Took side, but even they were not encouraged in their friendship by their elders.
Of course, as it says in the beginning of the tale, we as readers are left to determine whether Bilbo has actually gained more than he has lost - and we come to the conclusion that during his adventures Bilbo has realised who he really is - a hero and an adventurer, and therefore has gained more than he has lost in losing his respectability.