"You may doubt that you can do this, especially if you are older. But ask yourself this question, If I offered you $1,000 for every verse you memorized in the next week, how many do you think you could memorize? Yet God says of his word in Psalm 19:10-11, "They are more desirable than gold, yes, than much fine gold; sweeter also than honey and the drippings of the honeycomb. Moreover, by them Thy servant is warned; in keeping them there is great reward." The real value of the word is far greater than $1,000 a verse. The question is, Do you believe this? Believing this will be the crucial motivation you need."
Check this out: recommended weekly memory verses for 2009.
Here's a little more motivation.