I was at a shower where we played gift bingo. Everyone gets a blank bingo board before presents are opened and fills in possible gifts, (ie- picture frame, "wedding night attire") as the bride opens her gifts you try to be the first one to get bingo.
Another possible game would be Scattergories with a special game board. Instead of "Object in a room" or "Countries" You could say "words to describe bride", "flower", "love song" "honeymoon locations" (You could also make a Disney twist- "Disney Characters", " WDW Ride")