Once I was fishing a remote... bog... heath... all grown in body of water... whatever it was, and a pair of otters came swimming up to me. I saw some motion a dozen yards or so away, and immediately froze. They were playing and rolling around in the water as they swam - somewhat lazily - toward me. I don't think they saw me at all, because they came up within a yard of me, poked their heads out of the water, sniffed, and then turned around and swam away - just as nonchalantly as they arrived!
I felt blessed.
Unrelated to fishing, but the last time I actually had a close encounter of the friendly kind, was when one year I was up in my treestand, holding my bow, and a chickadee lighted upon my arrow shaft. He did one little chirp and flew away. I could care less about taking a deer after that happened!