In United States law:
This has not yet been tested in court.* A related concept is email confidentiality notices whose efficacy is considered, at least by the Wikipedia's references, not well grounded.
However I propose that by inspecting the language of the CFAA (Computer Fraud and Abuse Act) we can determine what email privacy is expected. While the CFAA does not address directly the question asked, it does show that legislation was constructed to map existing property and privacy law for physical items onto digital property.
A famous example of this is "logging into an unsecured server is illegal if you do not have permission to do so." The real world analogue to this is entering an unlocked house. It's still trespassing if you could be expected to know it was a private area.
* The only useful thing that can be said.
In this specific case:
If you receive a physical letter addressed to someone who is not you, you are not allowed to open it.
So, If you receive a digital letter addressed to someone who is not you, you are not allowed to open it.
This is complicated by how email actually works. You will open the letter by receiving it. I suspect what that means is that it is your duty to not act on, forward, or publicize that information that was sent in confidence. Your ability to do a thing has little bearing on whether you are actually allowed to do it (see: murder), and misunderstandings of that fact have let to outrage directed at the CFAA and hacking trials which I believe is misplaced.
I dislike the CFAA and conversations such as this one for a different reason -- people try to separate the physical and digital even though we have tons of existing precedent that covers both with very little imagination.