Every time I've been in a car over the Coronado Bay Bridge between San Diego and Coronado I've had to bury my head and pretend I wasn't on the bridge. Similarly, when I was in Tacoma on business in 1997, I told people if I had to drive to the Gig Harbor site (which I never had to), I'd be a bit longer since I'd take the long way around using the ferry to Vashon and then to Gig Harbor, rather then drive over the Tacoma Narrows bridge -- even if it wasn't the same one in the famous film.
What is odd about this, is that I have no problem being on the same bridge if I'm walking. For example, the last time I was in the Seattle area (1999) I was able to walk nearly half way out the bridge over Deception Pass to get some decent pictures, but then had to psych myself up to driving over it to get home.
Another odd aspect is that I find bridge engineering very interesting. For example, I would not mind walking out on the newest Tacoma Narrows bridge (if I were in the Tacoma area when it opens in a few weeks) to look at how it was made -- as well as the view from it. But I don't think I could drive it myself -- and might not want to be a passenger in a car driving over it.