I don't usually shake when I catch a good one, but if I'm in a tournament, or if the fish is a true giant (see avatar), I shake like a leaf.
My most recent experience with the jitters was when I caught a fish over 5lbs, on a drop shot, with 8lb test leader, on Kentucky Lake, on the final day of the high school national championship. She ran around a stickup and I had to chase her down and unwrap her, then she jumped 4 times after that. When I held the fish, I turned and said to my partner "We might have a shot at this thing". Nothing better!