As this NYTimes.com essays argues in The Case for Memorizing Poetry, there are lots of benefits to it. And before you write the idea off, consider these two mythbusters:
Myth No. 1: Poetry is painful to memorize. It is not at all painful. Just do a line or two a day.
Myth No. 2: There isn’t enough room in your memory to store a lot of poetry. Bad analogy. Memory is a muscle, not a quart jar.
A good and cheap way to improve your life. Shakespearean actors do it all the time. Why not you?
Smart People I Know 
Neat (& vg) idea! : )
Ever notice how you can still remember the poems/songs that you learned in grade school?
I believe it’s generally true that there are specific stages in our development when things that are committed to memory, actually “stick” there better & can be recalled more easily than stuff that you’ve learned later.
The exercise of memorizaton is actually very important, because as we age, short-term memory becomes poorer. Therefore using that part of our cognition helps to keep our brain in better “shape”! (Gotta keep those synapses firing! ; )
Indeed! It could be considered the beautiful exercise.