All Steel contains Nickel because it's an alloy; but Nickel is the MOST common cause of rejection (when the body pushes the jewelry out!) and allergic reaction.

316LVM implant grade stainless steel has one of the lowest occurrence rates of allergic reaction and/or rejection of any metal. The allergies people experience with stainless steel are usually nickel allergies, and the higher the quality stainless steel the lower the nickel content. 
Other metals can be poisonous when put into new piercings (silver) or even porous enough to hold bacteria (niobium, although for some reason this metal is continually used as a cheap alternative for titanium). Be sure to ask your piercer what is the best option for you and your piercing.

This is a quote from a pamphlet from Anatometal:

"The term 'surgical stainless steel' is not a technical term. It is a term that was originally coined by knife and cookware manufacturers. It brought more marketable value to the material that they used. 'Surgical stainless steel' is a generic term for a variety of different grades of steel and is not commonly found in any medical or metallurgical reports. There are no standards set for this type of metal.
"'Implant Grade Stainless Steel' is a more accurate term for the steel used in body jewelry. There are standards set for what materials can be called implant grade. There are currently only two different types of stainless steel that commonly match these standards: 316L and 316 LVM. these materials have been employed successfully in human implants that are in contact with soft tissue and bone for more than a decade.
"316L and 316LVM: Designations for types of steel that meet the standards for 'implant grade'. 316 is the designation number. The 'L' in these two designations stands for low carbon. the 'VM' stands for vacuum melted. Both of these materials meet the ASTM (American Society of Testing and Materials, a non-governmental organization that compiles information and makes standards for manufacturing, materials, and methods for just about everything) designation F138 for 'Implant Grade Stainless Steel' and the ISO standard 5832-1 and 6892 for 'Surgical Implant Material' and 'Requirements Against Nickel Allergies'."
In short, anything that says "Surgical Stainless Steel" isn't what you think it is. Granted implant grade stainless steel is usually a bit more expensive, but this is your body we're talking about. Would you rather put something in your body that is used in human medical implants, or something from Claire's?