Okay, sorry I like the diaper game too! ;) It is gross, but funny, especially for a first time mom! If it is a subsequent child I probably wouldn't do it. The ice melting game and the Price is Right sound super cute, I've never heard of those before!
I have done the guess how big the tummy is game and that's usually fun, another one I like is the left/right story. You can use a stuffed animal or a diaper or a bottle, whatever really, and then read the story and each time it says right or left, pass the object that direction. The person who's holding it at the end gets a prize and the mom to be gets the object. You can google the story and find one.
Another one I did was a make the baby name game. The mom-to-be didn't have a name picked out (this also works if you don't know the gender yet) so I got a box of Alpha Bits cereal and gave each person a baggie of letters and a paper plate. I put 5 mins on the timer and the person with the most creative list of names won. You couldn't reuse letters but plenty of people traded and bargained for letters they wanted! It was pretty cute.
Personally I do like games, just a few. I think it's a good idea especially if you have a bunch of people that maybe don't know each other. I would only do a few and then of course have chatting, eating and present time, but using of mix of interactive games and ones that you can just set up and leave (baby food and price is right) are good too b/c it gives people something to do as they are coming in and looking around.