AP:
Singapore and South Korea advised their citizens Tuesday against traveling to Thailand, raising concerns that the ongoing political crisis could damage the country's crucial tourist economy.
The advisories follow Prime Minister Samak Sundaravej's decision to impose a state of emergency overnight after clashes between pro- and anti-government protesters left one person dead and dozens injured.
Singapore and South Korea issued advisories urging their citizens to postpone nonessential travel to the country. Australia and New Zealand, on the other hand, advised their citizens to "exercise a high degree of caution" if traveling to the country.
"Travelers should exercise a high degree of vigilance at this time because of the political unrest," Australia's Department of Foreign Affairs said on its Web site. "Further violence cannot be ruled out."
BP: With the greatest respect to Singapore and South Korea this is a bit of an overreaction. That high degree of vigilance or similiar bureaucrat speak has existed for terrorism for a long time for Australia. It is the threat of lawsuits which has lead to the overreaction. My advice is you are more likely to suffer an injury in a traffic accident - particularly on a motorcycle (not wearing a helmet, driving drunk, and driving in the Islands of course add to the risk) - than to suffer any injury from political violence in Bangkok.
Basically, excercise common sense. If you see lots of people gathering together and they are carrying sticks and knives, it might be a good idea to go in the opposite direction.
The British:
# A State of Emergency has been declared in Bangkok on 2 September 2008. Gatherings of five people or more are prohibited. If you are in Bangkok, or have plans to travel there, you should keep yourself informed of developments, including by regularly checking this advice and the media.
#
Major demonstrations are taking place in central Bangkok. There have been outbreaks of violence, including clashes in the early hours of 2 September resulting in the death of one demonstrator and injuries to around 40 others. There is the possibility of further violent clashes. You should exercise caution, avoiding any demonstrations or large gatherings of people. See the Political Situation section of this advice for more details.

Just to add, the Swiss are in line with the British, Aussies and Kiwis. They also advise travellers to follow the advice of the local authorities in general. Additionally, the Swiss warn of possible strikes which could disrupt transportation.
I just read in the Swiss news that the Swiss travel agencies have reported zero cancellations as of now.
I wouldn't recommend people to visit Thailand from abroad at the moment unless they have a fall-back plan for getting stuck wherever they happen to be staying. The risk of violence probably isn't (much) higher right now, but the risk of serious inconvenience would seem to be. Why waste precious holiday time on a place that might fall apart?
I agree with Robuzo that the inconvenience factor could be considerable if road blockages continue or plans for strikes materialize.