A full image of a heart branded with the initials of you and your partner can be split into halves, and each half can be tattooed. Consider having the half with your initials tattooed to your partner, and have the half with her initials tattooed to yourself. They don't each have to be in the same spot, though it might make for a for more powerful symbol of your relationship if they are. The heart, itself, can either be the image of a human heart or the less graphic Valentine's heart.
You and your partner can sign a blank piece of paper, and any tattoo artist can easily copy the image and transfer it onto your body in tattoo form. This way, a part of your body will always bear your partner's signature and a part of his body will always bear yours. Sign the paper multiple times, and choose the best representation of each signature before having them tattooed. Popular spots for a name tattoo are the back of your neck, your inner biceps or over your heart.
Two turtledoves nestled together to form a heart can be a good matching tattoo for you and your significant other. The two doves can be represented on their own, perched on a branch with both your initials carved into the wood or suspended in air, carrying an initialized ribbon in their talons. Place this tattoo almost anywhere on your body, but the more extravagant the tattoo (i.e. with banners or branches), the larger it will be and the more space it will require.
For a puzzle pieces tattoo, you and your partner need to pick an image you both hold dear. It can be almost anything — a tree, a fish, a flower — provided it has significant meaning to the both of you. Then, split the image down the middle, simulating the edges of a puzzle piece, and have one side tattoo on your body and the other on your partner's body. The same spot on both your bodies can represent a stronger bond.