My wife and I have looked into this quite a bit as we've considered setting up a US based non-profit to benefit Belize. Anyone can establish a charity in the US and that charity may be for the benefit of anyone inside or outside the US. A foreign charity though must establish a US based non profit corporation and register that non-profit with the IRS. It's really not that expensive to establish, but there are reporting requirements that must be kept up and if you are having boards and members, then you have the normal politics involved with non-profits to deal with. Total cost to set up is around $1000 unless you want to get lawyers involved.
What I want to do is pretty cool but involves writing some software to guarantee transparency and unfortunately will probably have to wait until I make some more progress on other projects.
There are limits on who and/or what may benefit from a charity. A 501(c)(3) with annualized income less than 10k has a $400 fee. Over that amount is $850. Those fees went up 1/3/10. Humane efforts nearly always qualify. See IRS Form 1023.