I've steered clear of this issue so far because I'm pretty ignorant on what is happening in Burma/Myanmar. This morning I spent quite a bit of time reading articles linked from here, and so I have some thoughts I'd like to share.
My first thought is that these non-violent protests by the monks are very, very positive. Actually, my very first thought was a reaction to the tendency of people in places like the US and the UK to want to fix situations like this. And I think it's kinda ridiculous that we think we have the right, responsibility, and ability to 'fix' what amounts to a revolution in another country. What irks me about this well-intentioned tendency is the irony of it--irony on many levels.
These monks know full well what they are doing, I think. They must be fully aware that they are risking their lives. And it does look like up to several thousand of them have been taken into custody and quite possibly executed. These are individuals who are clearly willing to sacrifice their own lives in standing up against an oppressive system. How many of us, comfortable in our consumerist democracies, can make the same claim?
Yes, these atrocities are outrageous, and have been happening for apparently far longer than is commonly known. Some of Snoopy's links indicate that whole villages have been burned to the ground, their populations disappeared. How are we going to change that? Boycotting the Olympics is one option, although I think wil makes a great counter-argument to that in the Beijing Olympics thread. Also I wonder if we don't also inadvertently deprive the Chinese people of something when we boisterously boycott this event.
We will not be able to bring about any kind of meaningful change through a cowboy mentality of regime change. The scenario being played out in Iraq makes it clear that leveling an entire nation to bring in democracy is futile, hypocritical, and completely unethical. And although no one is advocating that approach for Burma, it seems to be the solution that we most gravitate towards in situations like this one and the recent atrocities in Darfur. A common response is to talk about putting pressure on officials (and actually do that), and even more common is to wonder why the UN doesn't step-in with a 'peace-keeping' force.
The clearest force for peace and change I see in Burma is these quiet, corageous protests by the monks. Let's not meddle with that. Even though it is extremely difficult to keep from squirming when the protests are stomped out by repressive governmental forces, I strongly feel that what is happening over there is extremely powerful and needs to play out as it will within that country.
Right now we are watching the most powerful force in the world--people united in spiritual solidarity--marching against the other most powerful force in the world, which is the brutal demon of a repressive, militarized nation-state.
Remember Gandhi. These monks may keep coming. I hope they do and my heart is with them! And the violence of repression may continue. We can see two different approaches, each highlighted and outlined by the contrast of the other. Is this is a time to choose sides between a militantly spiritual non-violence and a fierce repressive violence? I think of Freedom Riders and staunch marches to the sea to procure salt, of going forward despite the fear of being shot dead or maimed or tortured, knowing that the answers can never lay in violent resistance. And I think,
"How long, Lord? Oh, how long???" 
I guess as long as it takes. History repeats, yet as wil is fond of pointing out, we are learning. It's a steep incline with lots of rockslides, and we ain't gonna make it to the 'top' until we stop dynamiting our way through the freakin' mountain.
Peace,
Pathless
