Maybe.  Here's the evidence.

In 1985, a censor's error let an item labelled "Aurora", with no further
explanation, appear in that year's Pentagon budget request, with a
reference to "production funding" for 1987.  It was located next to the
operating budgets for the SR-71 and U-2.  The Pentagon refused to comment
on the item, and it has never been mentioned since.

In 1986, the US government sealed off large areas of land around the top
secret Groom Lake base in Nevada.  Many new buildings have been built at
Groom Lake during the 1980s, and intense activity continues.  The
government is currently (mid 1994) in the process of taking over more large
areas of land around the base, in order to make it impossible to observe
the base from publicly accessible land.  The extensive security measures
imply that some very important and very secret activity is going on there.
Officially, the USAF won't even admit that the base exists.

In February 1988, the _New York Times_ reported that the USAF was working
on a stealthy reconnaissance aircraft capable of Mach 6.  The story was
attributed to "Pentagon sources".

In August 1989, Chris Gibson, an oil exploration engineer and former member
of the Royal Observer Corps, was working on an oil rig in the North Sea
when he saw an unusual formation of aircraft pass overhead.  It consisted
of a KC-135 tanker, two F-111s, and a fourth aircraft of a type that Gibson
(an expert on aircraft recognition) had never seen before.  Seen from
below, it appeared to be a perfect triangle, slightly larger than the
escorting F-111s, with a leading edge sweep angle of about 75 degrees.  It
was completely black, with no visible details (unlike the F-111s), and
appeared to be taking on fuel from the KC-135.

In early 1990 the USAF retired its fleet of SR-71 reconnaissance aircraft;
the official reason given was that satellites could now perform all
strategic reconnaissance missions required by the Pentagon.  Many observers
consider this explanation to be suspicious, for several reasons.  First,
satellites exist in limited numbers and fixed, predictable orbits; surely
there will always be a requirement for high-speed reconnaissance missions
at short notice, which could only be performed by an aircraft like the
SR-71.  Second, the cost of running the SR-71 fleet was only about 7 per
cent of what the Pentagon spends on satellites; it would still be a good
investment even if only as an emergency backup.  Third, the USAF never
raised the slightest objection to the plan to replace manned aircraft with
unmanned satellites, which is highly unusual behaviour for an organisation
composed almost entirely of pilots.

At about the same time, _Aviation Week_ carried reports from witnesses who
had heard an incredibly loud aircraft taking off from Edwards Air Force
Base in California late at night.  Some of them referred to a pulsing sound
with a period of about one second.

On several occasions from June 1991 to June 1992, sonic booms were heard
over southern California.  They were not produced by any officially
acknowledged military flight (which are always careful to remain subsonic
over urban areas).  The booms were powerful enough to show up on the
seismographs operated by the US Geological Service, and the times of
arrival of the sound at various points allowed fairly accurate calculation
of the course and speed of the aircraft responsible; the USGS had already
demonstrated this by tracking incoming space shuttles.  The aircraft were
headed northeast, over Los Angeles and the Mojave Desert, towards either
the Nellis Air Force Base in Nevada or the nearby Groom Lake base.  The
speeds involved ranged from Mach 3 to Mach 4.

In February 1992, _The Scotsman_ reported that an RAF air traffic
controller, in November 1991, had seen a radar blip emerge from the base at
Machrihanish, Scotland, and quickly accelerate to Mach 3.  When he called
Machrihanish to ask what had happened, he was told to forget it.

In May 1992, a photographer snapped some strange contrails over Amarillo,
Texas; the trails appeared to have been produced by a high-speed aircraft,
and resembled "doughnuts on a rope".  A few days later, similar trails were
reported over Machrihanish.

All this appears to add up to a hypersonic aircraft, with a cruising speed
around Mach 6, being operated by the USAF from Groom Lake, Nevada, Edwards
AFB, California, and Machrihanish, Scotland, since about 1988
(Machrihanish, by the way, is due to be closed in 1995).  The aircraft
described by Chris Gibson matches several design studies of hypersonic
aircraft in the 1970s and 80s, which came up with a triangular planform
with a sweep angle of 75 degrees.  The engines appear to be rocket based
combined cycle (RBCC) engines, an advanced hybrid of turbojet, ramjet, and
rocket.  Unclassified studies from the US, Japan, and Russia have
investigated RBCC engines for hypersonic propulsion; such engines would be
extremely loud on take-off, would produce a pulsing sound with a frequency
on the order of one second, would leave contrails resembling "doughnuts on
a rope", and should theoretically have a maximum speed not far above Mach
6.  The most likely fuel for an RBCC engine would be methane; given the
assumptions of methane-fuelled RBCC engines, Mach 6 cruising speed, and
intercontinental range, the resulting aircraft would indeed be about the
size of an F-111.

Does this aircraft exist?  We don't know for certain, but the
circumstantial evidence is certainly persuasive.

Incidentally, the aircraft (if it exists) is almost certainly not called
Aurora.  Even if the mystery item in the 1985 budget did refer to this
project, the name would probably have been changed after the security leak.
But Aurora is the only name anyone has, so we continue to use it as a
convenient label.

Recently (mid 1994) there are moves afoot in the US Senate to reactivate
three SR-71 aircraft (possibly in connection with the Korean situation).
It was reported (from what sources is unclear) that the Blackbird successor
programme had collapsed "after consuming several hundred million dollars".
This has been interpreted by some to suggest that the "Aurora" was a
failure.

Ben Rich, who replaced Kelly Johnson as the head of Lockheed's "Skunk
Works" and was responsible for the F-117) recently wrote a book (sorry, I
don't have the title or publisher) in which he stated that "Aurora" was the
codename for Lockheed's entry in the ATB contest, lost to Northrop's B-2
(see section B.11).  I'm told that the book is careful to make no mention
of any SR-71 successor, either to support or refute the idea.

The best we can say at the moment is that the mystery remains open...

[Most of this information comes from Bill Sweetman's book _Aurora_]