I just hosted one yesterday! And we had games, but it was a "couples" shower, so it might be a little different than yours. I am not a fan of "bridal" showers.
We had trivia games mainly because that is something the couple likes to do themselves. But everyone had a great time from what I can tell. We had a multiple choice/fill-in-the-blank trivia game which loosely related to the couple--people played in groups. And a "newly-wed" game with all the recent and soon-to-be married couples-about 5 of them. And also a large cube with 6 pictures of where the couple had been, and people had to guess the landmark and city. So some games were organized and some were just sitting around for people to play.
So there were distractions around, but you could chose what to participate in. I think this works best. The prizes were all games and toys from Marbles, so they also tied into the theme.
And we skipped the opening of gifts entirely--I think that is usually the most boring part. Why are people all oohing and ahhing over gifts they requested! And that all the guests already saw on the registry!
Also it doesn't hurt to have some beer and wine around! I think even the guys had fun:)