The news both from Myanmar and China is hard to imagine. But at least in China, we know what is going on, and we can see that the government is doing something.
I always donate money after big earthquakes, in Japan and in other countries. It's a kind of superstition--if I donate the money, the big earthquake won't hit here. And of course, I donate for other reasons...tsunamis, and this time, typhoons. But this is the first time I have made so many donations in such a short time. First, because of the sudden rise in food prices, then for typhoon and earthquake victims.
For international situations, I usually donate through Mercy Corps, because they have partnership with local NGOs in many countries, and they are also rated very highly as a charity for which a relatively low percentage goes to overhead and a high percentage to actual aid.
For donating to disasters within Japan, there is always something set up through the post office (actually, for big international disasters too). Almost no one has checking accounts here, so postal money orders are a common way to send money. They always announce the postal accounts to send money to on the news, both for domestic an international emergencies; I used to try to quickly write them down, but I them discovered that the post office has a list of them. All you have to do is go there and say "I want to send money to X", and they'll show you the list of organizations collecting money.
It's really depressing to have so many natural disasters in such a short time...and the situation in Sudan getting even worse, with a possible war between Sudan and Chad.