This depends entirely on whether or not you have a fear of heights. I know several people who haven't enjoyed their drive all that much because of a fear of heights, but most people love the road. There are barriers along the way where there are steep drop-offs and plenty of room to stay in your lane. If you really don't like the feeling of a drop-off, you can always drive Going to the Sun Road starting at St. Mary's and ending in West Glacier. That way you'll be hugging the rock cliff side all the way, the furthest away from the drop-offs.