We have seen deer a number of times while out on our adventures, usually up close and as a complete surprise. More often, we see the evidence that they are nearby. My oldest is fascinated by footprints.
Maybe this doesn't quite count because they are contained, but there are a couple of local preserves where you can see Buffalo. They are always impressive and invariably start the girls singing "Home on the Range".
One of my favorite things is hearing my girls giggle after something has unexpectedly crossed our path. Those encounters can't be planned, and I'm glad! It would spoil the fun to have control over every detail.
Speaking of encounters...I nearly stepped on this Garter basking on the path yesterday. I shrieked like a little schoolgirl; not because I am afraid of snakes, but because it started me so much. The girls have seen me hold snakes much larger than this one, so they laughed at me. It was completely embarrassing. A short time later, we saw a juvenile Fox snake, but it was faster than I was with the camera. And No, I didn't scream that time.