My girlfriend will ask me to just put the camera down for a while and enjoy the experience, but I am one of those people that enjoy it more with a camera in hand.
For one thing, looking through a viewfinder makes me take in more of the details of the experience and forces me to really pay attention. This makes it easier to remember details of the experience for a long time. I remember visiting Seagrove Beach, FL and visiting the area where Eastern Lake flows into the Gulf of Mexico. The details of the sun going down, the boat on the beach, the birds, etc.. all are etched firmly in my memory.