Although grasping begins early it becomes better established during the last trimester. Babies grasp hands, feet, fingers, toes and, most commonly, their umbilical cords.
My ten year old was even impressed by those ultrasound pictures.
I remember when I was pregnant with my now four year old son I saw a really clear pic on the old 2D machine. My son was sitting there smacking his lips. It was so cute to see. I commented that he looked a lot like my husband as a baby. (from baby pictures) Once he was born the first thing my mother-in-law said was that our new son reminded her of my husband as a baby.