By “biggest”, this could either mean attendance numbers, or by historical/cultural significance. For example, Who has been to Woodstock, The Superbowl, The Olympics, presidential inaugurations, New Year’s Eve in Times Square, etc.?
As for me, I can’t really say that I have attended any big events beyond those of local interest. Events around Idaho’s Centennial celebration in 1990 was probably the biggest in terms of historical significance.
I was at Woodstock '94.
Lemme tell you, there’s nothing quite like walking amongst a crowd of a quarter-million people when you’re wearing nothing but sneakers and a strategically-placed fanny pack.
In terms of attendance numbers, I’d have to say Halloween in the Castro, which looks something like this:
http://insanecats.com/images/castro_halloween.jpg
and goes on for street after street.
November 4, 1995; well over 250,000 at (what is now known as) Rabin Square. The Peace Rally at the end of which Yitzhak Rabin was murdered 
Cal Jam 2 at Ontario Motor Speedway. Poorly run and over the top security. You couldn’t fart without someone threatening to have you tossed out.
Dallas Cowboys @ LA Rams in Anaheim Stadium. Probably 65,000 to 70,000 in attendance.
Well, I didn’t really attend, but I just happened to be in the neighborhood when thousands of angry Chinese students decided to throw rocks and lock down the US Embassy in Beijing after the Chinese Embassy in Belgrade was bombed.
Also, I happened to wander into an anti-war protest in Barcelona in early 2003. I’m pretty sure there were hundreds of thousands there. I was looking for a good tapas place.
Olympics, Atlanta, '96. At the end of the day when all venues had just emptied, those were some relatively sizeable crowds.
The 1986 EDSA Revolution that deposed Ferdinand Marcos and installed Corazon Aquino as president of the Philippines. Spent the night on the street; we couldn’t really sleep as there was always the threat of being crushed under tank treads.
Peter Frampton and Yes at JFK Stadium in Philadelphia. Police estimates were that 130,000 people were jammed into the stadium. You could barely walk across the field for all the people sitting on the ground.
Bay to Breakers yesterday had about 60,000 people. The last Giants game at Candlestick Park had about the same amount. I’ve done Halloween in the Castro several times now.
Apparently there were about 800,000 at the Golden Gate Bridge for its 50th anniversary.
The largest event that I’ve been at was possibly the largest demonstration on the Washington D.C. Mall: the March for Women’s Lives helf on April 25th, 2004. There were a million people there, more or less – and that estimate seems about right to me.
I attended a mass wedding of members of the Unification Church in Madison Square Garden in July of 1982. 2075 couples were blessed that day – I have no idea how many people were in the, um, audience.
Canada Day celebrations in Ottawa a few years ago. I don’t know how many people were there, but Parliament Hill was totally crammed with people enjoying the free concerts.
Michigan versus Iowa (college football) at Michigan Stadium at least ten years ago. 110,000+ in attendence, zero historical significance.
I did attend what was then the largest political rally in Dayton (OH) history when I saw Bill Clinton speak in 1996. It was a crowd of about 35,000, but we were only 30 feet from the podium. I remember thinking it was one of the most inspiring speeches I’d ever heard, but two days later not remembering a single word of it! It was kinda cool to see guys dressed all in black on the roof of every building in sight.
1993 World Youth Day in Denver. Wikipedia estimates 500,000 in attendance at the final mass.
I’ve been to many well attended football games (c. 100,000), but none that are significant.
I recently attended the consecration of the 11th Episcopal Bishop of Tennessee. That might be interesting if you are an obsessive devotee of apostolic succession in the Anglican church.
Just went to the Beale Street Music Festival. There had to be 200,000 people there.
Culturally signifcant: Game 4 of the 2004 ALCS: Yankees at Boston.
I was at Woodstock in 1969, when I was 17. I was there all three days, all the way through to Hendrix’s *Star-spangled Banner * on Monday morning.
I was at anti-war demonstrations in Washington in November 1969 (600,000 participants) and in May 1970 against the Cambodian invasion (100,000 participants). I got tear-gassed at the first one.
I went to New Year’s Eve in Times Square once, about 10 years ago.
Times Square New Years Eve 1999 to see in 2000. I was only gonna do it once, so that was the time to do it.