I pick one particular outing (fishing backpack trip) because of a large family of timber rattlers; just like saying hello to the fam., and coyotes and deer. I like the larger critters.
Love seeing bears too; although while i was day-hiking from camp about 8 months ago a young black bear wandered in and tore up my tent (lots of stupid-me lessons I could relate, but I digress...). I returned and caught him red-handed and he ambled off, looking back at me as if to say "so what are you lookin at?).
THE biggy for me on all forest trips is owls. Must listen to owls - they fascinate and relax me. In the desert it's coyotes carrying on at night.
Then, on water excursions, love the bald eagles, osprey (in particular), herons and cormorants. I look for them. I'm down south so don't get to encounter loons, but used to spend time 30 years ago in northern lakes and I loved the loons. I do get hawk migrations and I love watching them.