"When I awoke, all that was left of my life there... was the flute I'd taught myself to play."
In 2368, Captain Jean-Luc Picard acquired a Ressikan flute through an experience he had related to a probe launched from the dead planet. Picard knew how to play the flute, as all the memories of a man named Kamin had been planted in his memory through the probe. Among the memories was the ablilty to play the flute. (TNG: "The Inner Light")
Picard considers the flute to be one of his most prized possessions. It represents, to him, an entire lifetime he lived in only 25 minutes. As of 2379, Picard kept the flute on his desk in his ready room aboard the Enterprise-E. (TNG: "Lessons"; Star Trek Nemesis)
The music of the Ressikan flute was not played by Patrick Stewart, but by Brice Martin.  The flute prop was recently auctioned off for $48,000, after being estimated between $800 and $1,200.