We played some good ones at our shower.
We did the "baby no-no" game where everybody gets a sticker/safety pin/clothespin at the beginning of the night & has to give up their pin (to the person who calls them on it) if they say the word "baby." The person with the most stickers/whatever at the end of the party wins a prize. It's kinda silly, but some people really get into it. Plus, it's one that happens throughout the whole party, so you don't need to plan extra time for it.
We also had some unlabeled baby food jars for people to guess the food inside. They could look or smell or taste (although it would be more of a challenge if you can't taste it). The person who got the most right won a prize. People seemed to enjoy that one & there were a couple tricky flavors (prunes, I think, and squash?).
One that I thought would be more serious than it was is the "name the baby" game. We took all the letters from my and dh's first and middle names & had people come up with baby names using only those letters. I thought the winner was going to be the person who thought of the most names, but there were only 3 blanks on the paper and we were told we had to judge the "best" name. We got some VERY silly ones, and it was really entertaining to read them all out at the end!
I really wanted to have people guess the stats (sex, birthday/time, length, weight), but for some reason we didn't do that & I just set up my own at expectnet.com.
Not really a game, but something else I liked was having everybody write down some words of wisdom or wishes for us and/or the baby. You could do just a blank book, but we did colored index cards (without lines) and then put them in a photo album. I liked that idea because everybody could work on theirs while we were opening gifts (that kinda gets old to watch) & then we could add photos from the shower into the same album.
I've been to a shower where you have to bring a baby picture of yourself & then everyone has to try to match them all up with the adults in the room. I thought that one was pretty entertaining, but you have to plan ahead & make sure the invitations tell people to bring a baby photo.