The Harrier can do it, and do it slowly, too. A pilot who knows what he's doing can make the thing stand on its tail and slowly rise up, nose over and accelerate down range like a heavy launch vehicle. I saw it done once by one pilot; I think he was a US Marine squadron commander. It's certainly not the standard way of flying Harriers.
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Neither of those vids show the takeoff from the side, so you can't really judge the pitch angle. They both show it from behind or above where it's easy to manipulate the camera angle and make it look vertical for dramatic effect. That second video has "TV movie music" over it, which is a surefire way to get me to thumb it down. I want to hear jet engines.