They have very limited effects, even more so when they happen in Washington. Strategically speaking, if I had planned a similar national mobilization, I would have picked New York or Philadelphia as the venue. The problem with Washington is that these types of protests hvae to compete with similar historical events. The local and national media will look at the event and say, "How does this compare to the Million Mom March or the pro-choice marches?"
Several other posters have elaborated on reasons for doing this kind of protest: it shows that there are many people opposed to the war, it shows other governments that Americans don't support the government, and it gets some media attention.
There are other ways to achieve those goals, but this past weekend we saw an example of how a risk averse sectarian party capitalized on the current sentiment. The IAC organized a similar protest in June 1999 against the War in Kosovo, but that only turned out a few thousand people. The IAC only turned out a few thousand for the anti-WEF protests last January. They are capable of organizing a turnout for a national protest, but this weekend's turnout was more a factor of general discontent than anything inherently wonderful about ANSWER's organizing skills.
And I think many of us understand that big protest alone don't create radical social change. If that were the case, the Left would have achieved the revolution in 1985. I think the emptiness of these low-risk, permitted rallies and marches became obvious when Seattle happened. Now that was a riveting week of diverse actions that many of us will remember for along time.
Chuck0
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"...ironically, perhaps, the best organised dissenters in the world today are anarchists, who are busily undermining capitalism while the rest of the left is still trying to form committees."
-- Jeremy Hardy, The Guardian (UK)