Those are called suckers. Whenever i notice these around my trees i just prune them off. I don't think their is much to do about them other than removing them.
Not sure what kind of tree you have, but it is usually best to prune them off as Greenthumb mentioned. If they are grafted trees and the suckers are coming out below the graft, they are from the rootstock not the tree you want. In any case, they will drain energy from the part of the tree you want to grow.