They now believe at least 100,000 people will die from this thing. As FannishWaldo noted, Doctors Without Borders is one of the few aid organisations already on the ground there, so if you're looking for a place to donate, a way to help, they'd be a good one to start with.
Reposting that link:
http://www.doctorswithoutborders.org/ Direct aid from the US government is still being refused - although the Myanmar gov't said it would be accepted, it's actually been blocked, and can not get in. Since the US is typically one of the larger providers of disaster aid, and has ships in the region, this is a pity. So US people looking to help should donate to an international aid organisation like, again, Doctors Without Borders. Others already in the country include the International Red Cross, Save the Children and UNICEF. All aid organisations are actively working to ensure that their aid goes to the people of Burma, and does not end up being siphoned off for the military rulers.
Update on the situation:
http://news.bbc.co.uk/2/hi/asia-pacific/7389541.stm