Lots of ideas! One good book with Memory Verse games is the Big Book of Bible Games by Gospel Light Publishers. I think they have a second one out now also, though I haven't seen it.
Relay games- write the verse out on index cards, one word per card. Make 2 sets. Divide kids into teams and have them hop, skip, jump, etc. to one end of the room and get one card. Repeat until they have all the cards, then put in order.
Dozens of variations: use clothespins to carry the cards. Put on slips of paper and insert into balloons -- pop the balloon to get the part of the verse. Just shuffle the cards and race to see which team can put in order first.
Aerobic Verse Review! Write sections of the verse on sheets of paper and attach to wall. Divide kids up so some are standing at each section. Everyone squat down. As you say the verse the kids standing at that section jump up to say it, then squat back down. Once it's all been said, each section rotates to the next section and repeat. VERY invigorating!
Hide the Verse: Copy the verse onto cards, 1-2 per card. Make two sets. Hide around the room. Have the kids find the cards and put the verses in order. It helps to write one set with a different color pen.
Erase the verse: Write the verse on the blackboard or white board. Say it together a few times. Erase one word -- say it again. continue erasing one word at a time until all the words are erased and kids say it from memory.
Circle Verse: Review the verse a few times. Stand in a circle and go around the circle having each child say one word of the verse.
Puzzle Verse: Take old puzzles with the pieces all intact. Paint the puzzle using spray paint. Once dry, use paint markers to write the memory verse onto the puzzle. Illustrate with appropriate pictures if desired. Let the kids put the puzzle together. Good arrival or finishing up activity. Good stewardship of supplies too!
Even more fun! Use big floor puzzles and you can hide the pieces around the room and have the kids find them first then put together.
Sing the verse. (may not work with all) Find a tune that fits the rhythm of your verse and sing the verse to it.