If I call GetCompent() a rigidbody is added. How do I check if the game object has a rigidbody? I do not want to add one.
if(GetComponent()!=null)
should do it IF the script is on the object you are checking for a rigidbody. if you are checking a game object other than the one you are running the script on it would be more like
if(Target.GetComponent<Rigidbody>()!=null)
where Target is a predefined gameobject.
using this script
this.gameObject.AddComponent<Rigidbody>();