Of course we have that right, but whether it is "okay", or not is more of an ethical question and cannot be answered with a simple "yes", or "no". It would depend on a multitude of factors, including your relationship with the sender.
For any "normal" communication: If you are the sender, it's always "okay". If you are the receiver, it's generally not "okay", especially if you were instructed that it was privileged or confidential......that is unless it was an unwanted or unsolicited communication, in which case you have to use your own discretion.
For any communication which crosses certain boundaries; including threats, information concerning illegal activities, pornography, intention of self harm, or even totally insulting or vulgar content, you certainly have the right to either "publish" or direct those to the appropriate "authority", in fact, you may be legally liable in some of those circumstances, but actually re-posting them on a public forum may be just as inappropriate as being the original sender of them.
Third parties only have the rights granted to them by the principles involved and should respect their wishes.
voilà
J