Unmanned spacecraft would have to be one of the Voyager probes that slingshotted around the sun (and a few planets?) on its way out of the solar system. Speed is amazing - dozens or hundreds of miles per second.
Railed vehicle - the japanese have fast trains but I'll say the french Tres Grande Vitesse (TGV). Unless it's a rocket sled like Widget suggested.
Manned air breathing craft - some experimental plane of some sort like Chuck Yeager flew (X-1 or X-5?)
When you say air-breathing, do you mean something terrestrial, or something that literally has an engine that uses air/oxygen? So a jet as opposed to a rocket?