Ha. Amnesty International is perhaps the only bigger scan than the Red Cross.
Yes. I make it a point to tithe 10% of my post-tax income, and split it 5% to religious (generally the shul I attend) and 5% to non-religious charities. I tend to be heavy on donating towards mentally disabled children because I think they are among the most misused people in the world.
As a rule, any national charity that advertises on TV or that your work (or school) collects for is a scam.
So the advice above re: smaller, local, is better.
You like animals? Donate to the LOCAL no-kill shelter.
You worried about domestic abuse? Find the LOCAL shelter. Go look at it (and make sure it is not just a political front) and then donate.
Etc. It takes a little work. All the charities I donate to are ones I've been on the board of directors or actually worked at.