Below is a second version of the bingo idea, but here you create your own array of pictures. You can make several different cards and let your kids compete (no, I don't want to get into a discussion about competition at church, thanks) for who gets the first 'bingo.' Take stickers for prizes.
PS. My copy says this came from the April 1990 Friend, but it doesn't show up on an lds.org search. The authors/artists listed are Sheri Witlock, Beverly Webecke, and Scott Greer.
The third activity came from www.ldsworld.com years ago. (They may have lots of good stuff now. Go and see.) This wordsearch of "Words You Will Hear at Conference" is clearly for kids who can read fairly well.
And, finally, a crossword puzzle. This is very dated. Note the questions about the Tabernacle rather than the Conference Center and satellite was only available at Stake Centers. Clearly it was written in Utah (or thereabout) since you could watch conference on TV long before BYU TV. But kids won't care.
Meanwhile, parents could take a few notes - maybe, if you are lucky - on what is said. I had my seminary kids fold a piece of lined paper in half lengthwise and write at the top left "What the Speaker Said" and above the right column, "What the Spirit Said to me." I found this really helped me with application of the principles being taught.
Karen has posted links to lots more on her October 2008 Conference blog post at http://karenspoetryspot.blogspot.com/