Obviously, wealthier countries should try to help less fortunate countries, but they're not really obligated to. The needs of their own citizens needs to come first, in my opinion. Furthermore, the unfortunate reality is that these countries can't rely on foreign aid forever. They need to also do more to help themselves instead of expect someone else to take care of everything.
However, in the case of a natural disaster, wealthier countries should do everything they can to help those afflicted to rebuild. I see that as being an exception to my prior statement.