I found these two great "scripture memory games" at a teacher's resource blog that Luanne Payne called my attention to. It's called Vibrant Christian Living. It's full of ads (aren't they all) and had many memory ideas mentioned at other sites too. Here are two unique ones I liked from their site with my own twists added:
Word Wipe Out. Write your memory verse on a chalkboard or dry erase board. Read it together. Then erase one word and read the verse again --filling in the missing word(s) as you go. Keep going until the whole verse is erased and you can remember it. Then pass the dry erase pen and have the kids add the ones back in one or two or three at a time (depending on how long the verse is).
Gotcha! Quote a verse incorrectly to your kids, omitting or changing an important word. Ask them to shout, “Gotcha!” when the moment they catch the mistake. Then have them quote the correct word to you before you continue.
You can also do a version of this by writing out the verse with some wrong words in it, and have each of them secretly write down the right words --then see how many they got right.
You can use funny wrong words like "then Godzilla..," and "then Jesus laughed out loud and said" and "Petunia said..."