I am not a proficient or experienced healer by any means, but I have had a few notable experiences that remain in my head as my own personal "evidence".
I had pretty bad acne in my teens and into the first few years of my 20's. I had recently read You Can Heal Your Life by Louise Hay, and one of Tony Robbins books (and a few others that were in that realm). I decided to blend some of the ideas together into a plan to get rid of my acne. I came up with a 10 minute visualization and went through it about 3-5 times a day. In two weeks my face and back were perfectly clear for the first time since I was a pre-teen.
My Grandmother was receiving hospice care at her home. It wasn't exactly healing, but the same concept. She was at the end of a ten year journey with cancer. Her body was too far beyond healing, so I decided just to do what I could to make the process of dying easier. I repeated a visualization of her and I walking along a beach (she took me to the beach often when I was young). I imagined that I was telling her how much I love her and that it was fine to move on when she was ready, etc. I just tried to send as much love and goodness to her as I could. A few days after having started the visualization practice, I overheard my mom and aunt discussing how my grandmother - as she slipped in and out of awareness - kept talking about some man on a beach. Apparently, she didn't know who he was, but he was nice and she was not at all frightened by him.
On several occasions, more recently, I have used a similar process to help my dog. In once instance, I came home to find her laying on the floor unable to walk. She would get up and try, but her back legs just would not work. She would drag them for a bit and then flop back to the floor. She was otherwise fine, so I repeated a healing visualization while I laid with her for about an hour. I eventually moved her to the bedroom and slept with her on the floor... attempting to keep the intent burning all night. She woke me up the next morning to go outside and was acting and walking perfectly fine. I'm still not sure what the problem was. No problems with her legs since.
There are a few more, but those are the ones that have always stood out to me.
-"You can't always get what you want, but if you try sometimes, you might find... you get what you need"