Even if you're given permission, this is a bad idea. If you don't have permission, well, it's possibly the easiest way to betray a person's trust. I'm absolutely not kidding here, people. Let's take an honest look at what could happen:
Without permission, you find out something you didn't want to know. Serves you right. She might not even have meant whatever it was she wrote at the time. He could have ulterior motives or just be ranting. You will try and try and try, but you can never treat the person the same as you did before you knew what they were thinking about N. Worse yet, you may accidentally or not-so-accidentally reveal this information to a third party, trying to conceal its source. Joke's on you, bozo: it will always get back to her (or him). Yes, always. The age-old dilemma about when to act on covertly obtained information springs up--suicidal thoughts, a crush, and cheating are examples that could be in anyone's diary--and if you act on the information, maybe you do some small good, but you're guaranteed to do someone some harm. Probably yourself.
Without permission, you find out something you did want to know. Hmm, need I say it again? Serves you right. Now you know he has a crush on you, and he wants to be more than just friends. But if it's his diary, you also discover the motives behind what you thought was just a friendly gesture. You may even find out about a sexual fantasy. Or, you may discover that you're right not to trust her--but she's obviously right in trying to hide her thoughts from you, you snooping shit. No matter what you learn, you run into the dilemma of how you can use the information without getting into a tangled mess.
With permission, you find out... anything. If anyone gives you permission to read their diary, run don't walk. You don't want to know. You may think you want to know, but you don't. Think about it this way: why would someone want you to read their innermost thoughts? It's a wonderful gesture of trust, sure, but they may have been writing the diary with an audience in mind, in which case, it's a lie. And yes, I think that people, whether they intend to or not, censor their daylogs here. A gesture of trust that is actually a lie--how paranoid am I? Very. Or, maybe it is all truth (as much as a diary can be), and they want you to read it because they want you to know something, to see some pivotal entry. If that's the case, ask them to read it out loud to you--they can edit on the fly and still get whatever it is off their chest. If it's an awkward confession of undying love, it's a lot harder for them to agree to read it out loud; they'll probably prefer to just tell you, which is the better way to handle it. Any shocking revelation is better handled through real social channels than from reading an emotional history of a person's thoughts.
Let me just say it one more time, in case you haven't been reading closely: No. Don't do it. I don't care how amazingly mature you're willing to be about it. I don't care if you weren't looking for it, you "just happened" to find it. "Just happen" to put it the hell back. It is Pandora's Box, it is Einstein on the Beach, it is Humpty Dumpty. You can't forget it, you can't ignore it, you can't unlearn it, and you can never completely earn back a broken trust.
Thank you, that is all.
And if you do read a diary without permission, don't leave any evidence behind, especially not a handwritten, signed note placed in between the pages you read that says "You don't know me as well as you think you do". You brick-witted moron.