We have a box system of index cards to learn and review our memory verses. I made custom tabs with plastic A-Z tabs from the store - sticking my own new labels on the front. The labels are...
daily, odd, even, mon-sun, 1-31, new, cards
Behind "daily" we keep our current verses that we are working on.
"Odd" and "even" are for ones that we review every-other day.
Then we have weekly and monthly review.
I keep new verse to learn that I have already printed behind the "new" tab. Then I keep blank cards behind the "cards" tab.
I have a Bible binder where I keep organized all of the different materials we are using to teach and train our children up in the Lord. I have a chart to keep organized which verses we have memorized, plan to memorize, have recorded, etc. I print our verse cards on the computer, and I'll sit down to print 20-30 verses at one time. So, this chart helps me to keep it all straight.
We have a family worship time each night. It is during this time that we go through our Scripture memory box. My husband leads us in a lesson, Scripture reading, we pray as a family, and we review our memory work. We are all learning the verse - the whole family.
When we are learning a new verse, we sing it again and again for our children to hear. Then we start having them fill in the blanks. It doesn't take long after that for them to start singing along for the entire verse. By day 3 they can usually sing the verse themselves - or almost themselves with a little prompting.
During the day, the kids and I sing verse randomly. When we need to challenge our children in their character or correct them for a wrong done, the Scripture is right there in our heads and theirs. The Scripture is given to us for "reproof, for correction and for training in righteousness." It is a blessing to have the Word in our hearts and minds so we can correct and train and encourage each other.
Some creative ways to make the learning experience fun:
Fill in the blank: Pause for the kids to fill in the next word or phrase
Buzzer: Sing the wrong words (make it silly), and have the kids buzz you - with the voices - when they catch you.
Move around: Challenge the kids to do a motor activity (example - stand on one foot) while you sing the verse through once. Each time you sing the verse, do something else (spin in the circle).
Freeze: Dance around as long as Mom/Dad are singing the verse. Freeze when they stop singing and until they start singing again.
Just a few ideas. I'm sure you'll come up with some other great, fun things to do with your family.