Several marble tiles next to our toilet are stained with urine. Is there any way to remove them? The marble has been stained for several years.

The likelihood of removing these stains is about the same as that of winning the lottery. I would suggest replacing them.
TIP If replacement is out of the question you may want to try a solution of digestive enzyme to eliminate the urine odor. Digestive enzyme is sold at pet stores and janitorial supply houses for eliminating odor from carpets. Apply this solution and let it stand for several hours. Once the odor is eliminated you may be able to remove the stain with a solution of 50% hydrogen peroxide.