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I couldn't guess it at all, but a local activist reported that there were people filling up four streets parallel to Broadway, and they moved north on all four streets. His estimate was a million people.

People started leaving the demo at around noon, and we left the area at around 4:30 pm, and the buses were packed. (The MTA made a valiant attempt, but it's impossible to move so many people in and out of an area quickly. Most people chose to walk.)

The LA Times says at least 500,000 people.

These are all pretty wild guesses. It's difficult to estimate crowd sizes without aerial photos, and even then it's difficult. All we know for sure is that the big anti-war march in Hollywood in 2003 was one big street filled with people, and this was four. This is one of the largest, if not the largest, public protest in American history.

(See this article about The March on Washington for numerical estimates of that event. http://www.abbeville.com/civilrights/washington.asp )

I say a million, maybe not everyone was there at the same time though. Tons of people in my neighborhood couldn't get on the buses or trains and didn't arrive until later in the day or maybe gave up coming at all. I saw many strangers carpooling, picking folks up at bus stops and such.
Spring, Broadway and Hill were all taken up by marchers. Main St and even Grand Ave had folks taking up most of the sidewalks.
It was an amazing day!

I heard from this one reporter that the police say it's about 1 million people. they were people on the bridge on top of the freeway. that place alone i say it was a good 10,000 to 20000. people on there car show solidarity too alot of honk for support. also, i went to the olivera street it was pack of people there too from restaurant to buying stuff.

Not only were Broadway, Hill, Spring, and Main filled, all the little cross streets had people in them. And the main difference as well was that, unlike the anti-war marches where you had some room to move, the people on Broadway were packed in, super tight. It was almost scary how compressed the crowd was. People were coming and going all day as well, if they estimate over 1/2 mil then I think it's safe to say there were a million people at the march. Insane.

I'm uploading a pic that shows how cramped it was on Broadway.