I think the answer depends very much on where you are.
except America in other continents giving the account and bank number (IBAN and BIC) is a (the most) common way to enable someone to send money to you.
Technically, no. There is very little security in the US for bank drafts. With your bank account routing number it is very easy for people to draw funds without your authorization. Another thing people can do is buy stuff online with "demand drafts". Essentially it works like a credit card number where the create an electronic version of a check to purchase things. There is generally no password, PIN or signature requirement.
That said, it is printed on every check you write so keeping it private isn't really practical. I'd make sure you trust anyone you give it to and watch your account statements closely.
An important thing to know is that a routing number isn't a one-way deal. If you give out the number for someone to wire you money, they can just as easily draft on the account.