Could a SR-71 be shot down today?
Could SR-71 be shot down today?


Theoretically yes. Modern day SAMs like the 40N6 that travel at speeds of Mach 6 can intercept an SR 71 within an operational range of 250 miles upto an altitude of 18 miles. Moreover, the hostile SAM will fire a salvo of missiles(at least 2-3). So the SR 71 will have to jam, drop decoys and out manoeuvre the incoming hostile missiles.Modern day SAM systems can be loaded with libraries of 3D shapes that can be used by the seeker to identify targets and threats.

S-400 and similar Russian/Chinese AD systems are meant to work simultaneously with ECM systems, meaning radars of enemy aircraft will be blinded  as 40N6 and 48N6 missiles zeroes in.

During the days of the cold war Soviet Air Force pilots were instructed to launch two rounds, a semi-active radar homing missile and a heat seeking missile.In this fashion the SR 71( or any other hostile aircraft) being targeted has a difficult problem as it must jam, decoy and/or out manoeuvre three or four tightly spaced inbound missiles

That being said getting in the general vicinity of an intercept is different from an actual intercept.

http://www.codeproject.com/Articles/19310/Hitting-a-Moving-Target-The-Missile-Guidance-Syste

From Jane's  Fighter Combat in the Jet Age : Page 116-117 “SR71 the Ultimate Target” 


  On June 3, 1986 an SR 71 was on a mission over the Barents Sea. Six
  Mig 31 Foxhounds, vastly superior to the Mig25 Foxbat,performed a
  coordinated intercept that would have subjected the SR71 to an
  all-angle AAM attack that even a combination of high-altitude
  maneuverability and ECM could not have defeated. Fortunately for the
  American jet, the interception took place over international waters,
  but the Soviets proved their point.


In fact,the SR 71 was retired once the USSR started deploying S 300 SAMs in large numbers.


  I've read that SR-71 had no missile defenses because it could simply outrun any adversary. Is this still true?.


That is not true. The SR 71 did carry a very sophisticated Electronic Counter Measure System(ECM) called the Defensive System

One of the first MiG 31 Foxhound pilots, Captain Mikhail Myagkiy, who had scrambled with his MiG-31 several times to intercept the US super-fast spy plane, explains in his book how he was able to lock on a Blackbird on Jan. 31, 1986:


  The scheme for intercepting the SR-71 was computed down to the last
  second, and the MiGs had to launch exactly 16 minutes after the
  initial alert. (…) They alerted us for an intercept at 11.00. They
  sounded the alarm with a shrill bell and then confirmed it with a
  loudspeaker. The appearance of an SR-71 was always accompanied by
  nervousness. Everyone began to talk in frenzied voices, to scurry
  about, and react to the situation with excessive emotion.


Missiles are faster and can sustain higher G loadings than SR-71.  Assuming that the SR 71 is flying at an altitude of  70,000 ft to 80,000 ft  it only needs to maneuver to out turn the missile, in order to  make the change in intercept geometry fall outside the missile's envelope. However, at extreme altitudes aircraft maneuvers are limited by stall buffet.

The SR-71 could fly a 7,000+ mile mission and the only segments of which are flown at sub sonic speeds  are the take-off, refueling  and landing. 

http://www.sr-71.org/blackbird/

http://www.sr-71.org/blackbird/diagrams/index.htm

http://www.sr-71.org/blackbird/diagr...conprofile.htm

The thing is the Soviets knew that in order for any Soviet fighter aircraft to intercept an SR-71 it had to be ahead of its known flight path. These were the tactics the Soviets deployed to even get a glimpse of the SR-71. They always knew when an SR-71 launch would occur because the KC-135 fuel tanker would take off first because the SR-71 had to be immediately refueled once airborne.