Greenpeace and Amnesty aren't too bad though.
The charities that you really have to watch out for are the ones that outsource their recruitment and money collection to private companies. I remember there was a charity that I donated to regularly and the guy asked me for my regular donation and I asked him how much of my donation went to the cause. Turns out 50% was going to his company's fees! Taking into account the actual charty's admin fees, overheads, etc. and it's certain less than 50% of what I was donating was acually going towards the cause.
Also if you do sign up to a charity, always make sure you read their privacy policy. As I said, often it's not the charity itself that does the recruiting, following up for money etc. but another company that does this. Often these companies maintain huge databases of people's information. So you may give your details to this company that's representing one charity, but when that company is engaged by another charity to recruit or get more money, they will also go after you too. So you might find yourself being chased by a charity you haven't even heard of or signed up for.
So yeah, specifically look at their privacy policy to see that it says "we do not give your information to third parties" or something to that effect.