The F-107 lost to the F-105. Scott Crossfield damaged #3 in an aborted takeoff. A/C #1 is at the Pima Air and Space Museum in Tuscon, AZ (I've seen it, and no, I'm not sure I would've wanted to fly it with that intake right above and behind the cockpit). Number two is at the USAF Museum.
It's strange because (according to wiki, at any rate) they were planning on having a chin intake at first, but moved it to the top of the plane. I mean, really.
Now, aircraft I would have liked to see fly--how about the Space Shuttle Booster "Aircraft" from the original TSTO Shuttle proposals? They had transatlantic ferry capabilities, IIRC (had to, so that they could get back from the TAL sites they would have landed at to Kennedy), which I should think allows them to count as an aircraft as opposed to just a rocket with some incidental flight capabilities.
Or maybe the X-24C hypersonic research aircraft that was proposed but not built in the late '70s? It would have explored an interesting flight regime. Of course, it might have as a black project, considering the circumstances of its cancellation.