A popular idea for a tattoo on the ribs is a word or words. The tattoo can range from a single word, like a name, to a paragraph or words, like a quote or a song lyric. If it is only a single word, than it would fit better if the word is tilted vertically to fit the lines of your body. If it is a paragraph of words, small letters running horizontally along the ribs may fit better in this situation. A licensed tattoo artist will help you decide which would fit better for what you have chosen.
Variations of trees, plants or vines are popular tattoos to get in this area. The reason for this is that they are all taller than they are wide, allowing them to fit proportionally down the side of the torso. People often get creative with what design they use, such as a vine, a branch with blooming flowers or just a cluster of flowers.
Often, you will see an image of a person or a cartoon figure on a person's ribs. These often fit well running down the side of the torso, because a person or cartoon figure is taller than they are wide. You could select someone famous that you admire, a loved one that has passed away or a favorite cartoon character.