Hinckley fired five or six shots at Ronald Reagan on March 30, 1981, as Mr. Reagan was walking to his limousine after addressing a labor convention.
The president was hit in the chest. Presidential press secretary James Brady was struck in the head. The attack left Brady brain-damaged and unable to walk. The attack later turned Brady into America's best-known crusader for gun control.
A police officer and a Secret Service agent were also wounded in the shooting.
Secret Service agents shoved Mr. Reagan into a limousine which sped him to George Washington University Hospital. He underwent surgery and didn't return to the White House until April 11. Mr. Reagan eventually made a full recovery.
Hinckley was indicted for the shooting, but was found not guilty by reason of insanity in June, 1982. He was given an indefinite term at a Washington mental institution.
On Wednesday, Brady, speaking in Washington with other gun-control advocates, pledged to continue the fight for tougher laws even though Republicans, traditionally more gun-friendly than Democrats, control the White House and Congress.
Brady's wife, Sarah, chairwoman of an gun control group called Handgun Control and the Center to Prevent Handgun Violence, said, "We've got more support now than we've ever had."
James Brady said 670,000 Americans have been killed by firearms since March 30, 1981, the day he and President Reagan were shot.
Brady blamed the National Rifle Association for blocking legislation to mandate child safety locks and close what's called the gun show loophole, which allows the sale without background checks of firearms at gun shows.
In response, the NRA said most Americans support the right to bear arms and don't want new laws passed. Instead, "more money should be spent to enforce the existing laws against violent criminals," said James Jay Baker, the NRA's chief lobbyist.
"No redesigning of political strategy can bring these anti-fundamental rights organizations into the mainstream of America," Baker said.
©MMI Viacom Internet Services Inc. All Rights Reserved. This material may not be published, broadcast, rewritten, or redistributed. The Associated Press contributed to this report