IMO free climbing is the only way to do it. I enjoy climbing trees, not ropes. I can climb 20 trees in a couple of hours and don't need to spend a dime on equipment. I personally enjoy testing the limits of my physical abilities to see whats climbable. Here's a video of me climbing some trees.
For trees with thin or no branches, you can bear hug up if you wear long sleeves and pants so the bark doesn't tear up your skin.