Trivia: As is often the case, the title for the film was changed in different countries, with some being humorously much more or much less "dirty" than the original title. Most notably, the title of the film in Singapore was briefly changed to "Austin Powers: The Spy Who Shoiked Me" (which basically means "The Spy who Made Me Feel Good"), while Norway's title for the film translates to "Austin Powers: The Spy Who Ejaculated on Me."
Trivia: The NATO soldier at the beginning who watches Jerry Springer, is played by Michael McDonald. McDonald was also in the first Austin Powers film as the henchman that gets ran over by the steamroller.
Trivia: The bit where Basil and Austin break the fourth wall and tell the audience to "not worry" about the time travel element and to "just enjoy yourselves" was evidently a spur-of-the-moment improv by Mike Myers and Michael York.
Trivia: The original film had not yet been released in South Korea when this sequel was released. In order to compensate for this fact, South Korean prints of this movie were accompanied by a music video that had a subtitled summary of the events from the first movie. The original film was finally released the following year as a "prequel" entitled "Austin Powers Zero."
Answer: It's called "Soul Bossa Nova", by Quincy Jones.
Grumpy Scot