Getting musician or band images are one of the more popular tattoos. Many bands have easily recognizable band logos. Fans that are more ambitious, however, can get images of the band members tattooed -- although this will be more expensive and painful. The risk of having your current enthusiasm poked into your skin is that your tastes will change, and if in ten years you are a passionate flamenco guitarist, you will feel a bit silly with a tattoo of an unrelated artist across your back.
Images of instruments make good tattoos. They are not as trendy as band names, making them less irrelevant in future years. Many instruments have beautiful lines and curves, lending themselves to graphic representation as in a tattoo. Some tattooists specialize in creating stylized images of musical instruments, some of the more interesting as anthropomorphized renditions of common instruments.
It is possible to have an entire musical score tattooed onto yourself, if you are patient, wealthy, and have a high tolerance for pain. This would be a way of showing total dedication to a particular piece of music. Performing as a living music stand and having someone play the piece off your body would make an interesting performance art work.
Heavy metal fans probably have more tattoos than the rest of humanity combined. If you are a serious metal fan, you really must have a skull, a snake, a dragon, a pointy guitar, and ideally, all four permanently welded onto a part of your body. A good piece of advice: avoid tattoos above the neck; you will regret it when you are 35.