Austin Powers series. According to the Word Of God, the Austin Powers series is a parody to all of the British James Bond-knockoffs in the United Kingdom in the late '60s and early '70s that Mike Myers used to enjoy, though there are plenty of James Bond references as well.
There's the shout-out that Austin made to the 1960's James Bond knockoff In Like Flint. While he's watching it, Austin even says "That's my favorite movie!" Years later, a magazine print ad for a DVD re-release of the Flint series gave a shout-out in turn by using that line as a pull quote.
Star Wars is frequently referenced in the second film as well.
The trailer deliberately misled moviegoers into thinking that it was a preview for the then-upcoming The Phantom Menace. Instead of Palpatine manning the Death Star, though, it's just a chair reveal of Dr. Evil. The following tagline echoes that of The Naked Gun:
"If you see only one movie this summer, see—! ...Star Wars.
"Anyways, the key to this plan is the giant laser. It was invented by the noted Cambridge physicist, Doctor Parsons. Therefore we shall call it... The Alan Parsons Project!"
The music during the intro when Big Boy floats past an astronaut is a parody of the soundtrack to You Only Live Twice.
It has an homage to Silver AgeSuperman and Lex Luthor going on, with Young Austin attending a spy "academy" with Number Two and an adolescent (and already-bald) Dr. Evil. When Austin wins the coveted International Man of Mystery award, Dr. Evil vows revenge.