Given enough time, yes, your tattoo will change some. If your skin sags, the tattoos on it will sag as well.

Your skin is your body's largest organ, and it is constantly shed and replaced. Since the dermis, the second layer of skin where the tattoo ink is deposited, does not shed like the epidermis does, you will not lose your tattoo. However, the tattoo will suffer some degradation as time goes by. The ink will break down a little and the tattoo will start to blur and lose some clarity of color.

If the tattoo was done well in the first place, this degradation will take years, even decades, to occur. At this point, it's possible to re-touch the tattoo, or even cover it up entirely with a new design.