Internationally and to a certain degree domestically in the US, Oxfam, Medecins Sans Frontieres (Doctors Without Borders) and Save the Children are all efficient charities according to CharityNavigator. There are likely others but these are three solid charities imo.
There are a few organizations that try to quantitatively evaluate charitable organizations and similar- notably (and off the top of my head), CharityWatch [1]. Donating based on their metrics (although not the irrefutable truth of the matter, likely enough) is likely to lead to better "returns" from a donation than going by brand/marketing power.
Notably, despite its prominence, Red Cross scores only a "B+" rating on CharityWatch.
Doctors without a frontier?
It's sad though, I think many europeans would like to donate money for people in need, but when you find out things like this ... Americans really managed to ruin this as well.
I don't think that's at all true. There are many large organisations that spend a significant amount on staffing and marketing, masquerading as charities. The state-sponsored ones are some of the worst, as they're recycling taxpayers' money to lobby the governments that pay them, with a revolving door of lucrative executive and lobbying jobs keeping it all afloat.
MSF/Doctors without Borders -> https://www.charitynavigator.org/index.cfm?bay=search.summar...
Save the Children -> https://www.charitynavigator.org/index.cfm?bay=search.summar...
Oxfam -> https://www.charitynavigator.org/index.cfm?bay=search.summar...