There is a lot of proof! Primetime covered the case of little James who remembered WWII and being a pilot shot down;- a lawyer, Angela Grubbs has documented her case as if ready to present to a court of law, a police detective Captain Robert Snow followed his memories to prove there is no such thing - he found his past life and proved himself wrong.
Carol Bowman has hundreds of children's cases in America - Ian Stevenson has thousands from all over the world. Carol Bowman has a great discussion forum - you should check it out. Tons of information.