I was thinking of putting this in Local Customs, because I have yet to hear of anything dangerous about these, but I guess a warning is warranted as I was caught in one on one of my first trips to Seoul. We were taking a bus to downtown and one stopped our progress. We were about 10 minutes from the hotel but had to stay on the bus (I now know that Koreans are a little too self-conscious and we could have probably gotten out and walked).
Most protests just block the road for a while and I've never heard of a recent ones that ended in any real police action (although that did happen before). If you'd like to hear one take a listen to the Audioblog on this page.
The main places for protest are: Yeouido (near the politics/National Assembly) and downtown (especially near City Hall and Seoul Station). Everywhere else is pretty free of distubance.
Seoul has frequent protests throughout the city, usually at the US military bases, the US embassy, or the Korean ministry of defense. Occasionally these protests will get violent, such as when the president was impeached in March 2004. You would probably be safest if you avoid these gatherings.
Say no to US cows no matter what they say to you.
The South Koreans (especially in Seoul) are known to do there share of protest from time to time. Lately the protest have been aimed at Japan and the American government. The majority of the participants in these protest are young college students. Most of them disagree with the US led war in Iraq and don't mind expressing their discomfort. For the most part the protest are peaceful and there is a very large Police presence. Contact your country's Embassy for a list of protests or check out the website below. It's against Korean law for protestors not to reveal the details of their protest before it takes place.
We experience the police preparing for a protest at City Hall, since we were staying at the Westin. I wish I was able to go see it but the next day we realize that there was almost 200,000 people at it. We could hear the noise from outside the hotel. I guess it had to do with laws. So I would say if there is a political thing going on that involves Koreans, just let them be.
Demostrations we saw around the US Embassy were mild.
I never felt scared or in danger at all, even with things going on around the street.
In general, Korea is a safe place for western travellers. However, there are reocurring student, political and labour demonstrations that, at times, can deteriorate into small anti-Western riots. The locations of these demonstrations are known in advance and, before heading out for the day, you may want to check with the hotel concierge/staff to see if there are parts of Seoul (or other cities) you may wish to avoid.
It is not uncommon to head demonstration in Seoul. Please stay away from the protesters because they may become very violence when the police troops arrive.