Some of the Cirque du soleil videos use the multi-angle feature. When an icon appears at the bottom corner, you can use the angle button.

Also, the James Bond Special Edition (the silver box cover version) of The World is Not Enough has a feature when you see the 007 icon at the bottom, you can use the angle button to show storyboard versions of the scenes while they're happening real-time, in a PIP window in the corner.

Another one that comes to mind is Animusic. It's not that well-known, but if you're into computer animation effects, check it out. As far as I know, you can only get it from their web site: www.animusic.com. I guess technically, this would be a special feature version tho, because you have to choose the option, then when you're in that mode, while the song is playing, you can choose a different instrument with the angle button.
Otherwise, like others have said, they're mostly just extras on the DVDs. I vaguely remember a concert video having this ability too, but memory fails me right now.