An organization outside of the USA (I'm in the USA) is going to wire money into my bank account and has asked for the following information:
Is all of this information safe to provide, or will this amount of information empower other people to withdraw money from my account?
That information is the only way to get money wired directly into your account so you don't have a lot of options. You should be reasonably comfortable giving out that information as there checks and balances (as noted above) but more than this the banks tend to err on the side of avoiding a PR nightmare if someone uses routing/account to defraud their customer.
For bank security you should be more concerned about
a) your credit card, only use secure https sites and ones you can see are dealing with lots of customers
b) your identity, someone with your social security number, a recent bank statement and some basic information about you (like family, birth location etc) can assume your identity
c) your bank login, be sure to create a strong password, pref 10 characters or more with numbers, symbols and upper & lower case. A site like http://strongpasswordgenerator.com/ can help here.
This is the information required to wire money into your account from abroad.
They would only need the account number and the ABA (routing) number to withdraw, and it is printed on every check you give.
In Frank Abagnale's book "Art of the Steal" the author talks about how to set up a bank account for safe wire transfers. He recommends setting up an account at your regular bank and specifying that money can be transferred into that account from another bank, and out to your regular account only. You are then free to give the necessary transfer information to whomever you want, knowing full well they can't take money out.
This guy should know what he's talking about since he's an ex-confidence man legitimately working as an American security consultant.
