The exact chronology of the U-2 incident is a bit more complicated, and much more embarrassing, than the one cursorily given above.
First of all, the U-2 planes were indeed carefully disguised as NASA "meteorological aircraft," including two actual press releases from NASA about the program issued before the incident.
Gary Powers was shot down on May 1, 1960. He was under orders to activate the plane's self-destruct mechanism in case of an emergency, but chose to eject without doing so because he feared (correctly?) that it would have activated immediately and killed him as well.
So, four days after Powers disappeared (and blissfully unaware of his capture), NASA issued a very detailed press release noting that an aircraft had "gone missing" north of Turkey. The press release speculated that the pilot might have fallen unconscious while the autopilot was still engaged, even claiming that "the pilot reported over the emergency frequency that he was experiencing oxygen difficulties." To bolster this, a U-2 plane was quickly painted in NASA colors and shown to the media.
After hearing this, Nikita Khrushchev announced to the Supreme Soviet (and hence the world) that a "spy plane" had been shot down. The White House, presuming Powers was dead, gracefully acknowledged that this might be the same plane, but still proclaimed "there was absolutely no deliberate attempt to violate Soviet airspace and never has been," and attempted to continue the façade by grounding all U2 aircraft to check for "oxygen problems."
On May 7, Khrushchev dropped the bombshell:
I must tell you a secret. When I made my first report I deliberately did not say that the pilot was alive and well... and now just look how many silly things they (the Americans) have said.
Not only was Powers was still alive, but his plane was essentially intact. The Soviets managed to recover the surveillance camera and even developed the photographs! Powers' survival pack, including 7500 rubles and jewelry for women, was also recovered. Khrushchev sneered:
Why was all this necessary? Maybe the pilot was to have flown still higher to Mars and was going to lead the Martian ladies astray?
This brought the 1960 Paris Summit between the superpowers to a halt. The US ended up with a lot of egg on its face, not just politically but also technologically, since the U2's altitude of 68,000 feet had been thought to be beyond the reach of the Soviets' SAMs.
In a somewhat ironic twist, in 1971 NASA was actually given two U-2s for research.
The wreckage of the plane in question is now on display in Ekaterinburg, the restored name of what was Sverdlovsk in Soviet times and the closest city to the shootdown site.
Trans-Siberian Handbook, 4th Edition