I'm giving a go at memorising them. I'm up to Psalm 18
If I read the Psalms normally, I just gloss over. It's all the same at first glance, like listening to Californian skate punk. Miry depths this, enemies like lions that, praise the Lord with the lyre the other. Potsherd. Selah.
But memorising forces you to slow down.
Here's a little verse that jumped out at me, something filled with great meaning from the point of view of the New Testament:
You give me your shield of victory,
and your right hand sustains me;
you stoop down to make me great.
Psalm 18:35