for me, it's the following...
The first day of rifle in the stand. Like others said, it's much different feeling.
Hearing the woods come to life as first light approaches.
Watching the squirrels chase each other around from tree to tree (although I hate it when they're so loud that you think it's a deer approaching)
Sometimes seeing a pheasant take off from a tree
Seeing turkeys come into a field or through the woods single file.
All the birds calling to each other throughout the day.
When on the mountain,the breathe-taking views in the fall during archery
Finally settling in your stand in the pitch black
Just relaxing in a stress free environment (at least it's stress free til your trophy appears lol)
Of course, your heart jumping when you hear a deer approaching
Your heart going up in your throat as you spot the deer approaching and unaware of you
Your particularness of when to raise up your gun or draw the bow when the deer is coming right toward you
Even if you end up with nothing at the end of the day, seeing a young kid with their first harvest proud as can be
The feeling of when the time is right to pull the trigger/release the arrow.
Seeing a non-shooter, but just appreciating being able to see them doing their own thing
This isn't in the woods, but when you harvest your animal, the satisfaction of enjoying a tasty steak or burger thanks to your precision marksmanship!
After your kill, wishing that your relatives that once hunted with you and passed on were with you first hand to experience it even though you know they are there in spirit
Thinking about real good times you had with those relatives that passed on while waiting for your targeted game species to appear
...Gotta love the sport, so much more than just killing!