As much I have tried, I have never been lucky enough to see a Grizzly in Yellowstone during our several trips there. Just the fact that the Grizzlies are near by though makes Yellowstone an exciting place. The dense Lodgepole Pine forests feel a lot more dangerous and mysterious when there could be a griz around the next bend.
Here is a good (and true) Grizzly story from Yellowstone. I have a friend who visited Yellowstone the week of Jun 18-23, 1995. They spotted a Grizzly in one of the large valleys and watched it for 3 hours. (above it, from the road). A whole group of people gathered with spotting scopes and binoculars. As the crowd watched, the Grizzly charged a herd of elk. The elk scattered and escaped the bear.
The unsuccessful Grizzly then meandered down to a little stream, and as the elk watched, he slowly rambled along the stream. Eventually he went behind some bluffs and dissapeared from the elk herd's view. The elk keep watching where they last saw the bear.
The Grizzly circled around some low hills, and approached the elk herd from behind. As the elk continued to watch where they last saw the Grizzly, by the stream, the Grizzly came charging over the top of a hill at full, Grizzly locomotion speed. He suprised the elk herd, and was able to swipe at one of the elk and disable its back legs. My friend said that it took quite a while for the Grizzly to completely bring the elk down, but that the elk could not run well, so it could not excape.
I still get a thrill when I hear this story, like I did the first time Joe told it to me.
When we camp at Yellowstone I sleep outside with my dog instead of in our travel trailer with my family. My dog has trouble sleeping because of all the noises in the darkness. Maybe someday one of those noises will show up as a Grizzly.