Were there many Gamgees?

[The Saucepan Man]

Neither Hamfast nor Sam were present at the Long-Expected Party as it is presented in the book. The guests in the tent were those invited to the special family dinner-party, and the numbers were restricted to twelve dozen. They were:

selected from all the families to which Bilbo and Frodo were related, with the addition of a few special unrelated friends (such as Gandalf).

I suspect, therefore, that the Gamgees were not as closely related to the Bagginses as those families that were present and that neither Hamfast nor Sam counted as "special unrelated friends", the relationship being (as has been mentioned) one of master and servant (albeit one which involved a great deal of mutual respect).

As Eomer has pointed out, the film does not play on the class divide and so the Gamgees (or Sam at least) were present at the party. The reason that they are not mentioned in Bilbo's speech is, no doubt, because they lifted the speech straight from the book (where no Gamgees were present).

[Encaitare]

It's true that the class difference isn't played out that much in the movies, although maybe audiences wouldn't have liked the master and servant relationship as much as two friends sticking together through thick and thin.

[Boromir88]

Encaitare I do agree, I think the master servant relationship would have had a negative effect on the audience.

[Eomer of the Rohirrim]

Well, that's the 21st century for you!

Saucepan Man almost nonchalantly provides the most sensible answer, and makes the rest of us wonder Why didn't I say that?

[Morsul the Dark]

Indeed I was at work and I had thought of that answer all proud I can to the Downs just to find Saucepanman already said it