-71 is the fastest airbreathing plane and, as Timz says, the fastest plane to take off under it's own power.
The X-15 is the fastest rocket powered plane.
And since no one has mentioned it yet, I will: Aurora.
NetJets is a fractional ownership company, meaning that you buy a certain share in the use of an executive jet. NetJets provides the plane including crew and maintenance. You provide the cash and can use a plane for a given amount of hours each year.
It's not really an airline in the traditional sense, but aren't charter airlines simply you buying a share in the usage of the plane? It's a fuzzy distinction at best.
"There are no stupid questions, but there are a lot of inquisitive idiots." - John Ringo