There are so many different tattoo designs for men and women on rib cage. It's quite a large area to get tattoo so use your imagination.
As for men, one of the most popular designs I've seen are script tattoos or word tattoos. Old English lettering tattoos with a cool looking handwriting or any other foreign languages like Latin, Arab, or Sanskrit which also have cool and mystic looking letterings. The general idea is to look for a famous quote that you like from a saying, poem, song, movie or something that is deeply meaningful in your life.
I've seen many men have rib cage tattoo designs like crosses, dragons, angels, swords, or even tribal designs. You can always combine those design together just be a little creative.
Script and lettering tattoos are also very popular for women, with the same idea as the ones for men above. Many women I've seen with rib cage tattoos including celebrities like Megan Fox with her famous rib cage tattoo saying: "There once was a little girl who never knew love until a boy broker her heart".
Many other really popular designs for women are flower designs like cherry blossom or Hawaiian flower tattoos also known as Hibiscus flower.
Stars tattoos are sexy for both men and women on the rib cage. You can do one or two stars or you can make it fill up the whole rib cage depends on your taste. Shooting star tattoos are quite popular and sexy designs; they stand for your memorable moment in life. Nautical star tattoos stand for safety and protection.
Bird tattoos could be a really beautiful choice for women tattoos. Swallow tattoos are popular and symbolize health, wealth, loyalty, and love to the family because the fact that swallows always return home every year no matter where they are. Swallow tattoo designs can also be combined with star, flower, or script tattoos.
Rib cage tattoos designs are popular yet can be hurtful to get. Most people I've asked said it's hurtful to tattoo on the rib because the bones are so close to skin with tremendous amount of nervous systems. However, don't let this stop you from getting your dream tattoos, just try to do something during this process. Make sure you get the right tattoo because nobody wants to go through all this pain and then regret getting it.