Try mirror exercises with a partner. Stand in front of each other. Your partner makes movements, such as moving his hands around, and you mirror those movements with your body.
Use a Rubik's Cube. This is a game played by moving around colors on a cube that is comprised of other, smaller cubes. The goal is to get each side of the cube all the same solid color. Attempting to solve the puzzle will help improve your spatial intelligence, even if you cannot solve it just yet.
Complete other jigsaw puzzles. Jigsaw puzzles require you to picture a finished picture and be aware of where the pieces go in relation to others, which develops spatial intelligence.
Learn strategy games that involve moving pieces, like checkers and chess. These games require you to picture how the board will look after you move your pieces, which will exercise your spatial intelligence.
Practice a musical instrument. Reading music and playing an instrument are ways to heighten spatial intelligence in adults.