The Quick and The Blue: The entire song is basically Quick Man trying to come to terms with his eventual death.
Programmed to Fight: Though ambiguous, it appears Crash Man commits suicide with his last ounce of will so that Mega Man can retrieve his weapon.
Promise of Redemption: Bubble Man's entire life was a joke, and he wanted to give his ridiculous existence some sort of meaning and respect by avenging the murder of his brothers. But we all know his death will be just as meaningless as his life.
Everything about Proto Man; his song I'm Not The Break Man is about his depression from being rejected by Light in favor of Mega Man. "I had a name, my father called me Blues," Light tearing his heart out to put it in Mega Man, and "I'm not broken; I'm not the break man". In the end, even Melody From The Past as he begins to accept his situation and forgive his family is heartbreaking. All the way through.
There is a song I hear, a melody from the past./When I woke for the first time, when I slept for the last./You are the one, the hero who will stand./Do not blame Father, he is only a man.
The Message From Dr Light, where Light is lamenting how he has to continuously watch his "son" go out to stop Wily, knowing this is his fault at least in part.
History Repeating, both parts, where Megaman laments his role in constantly having to stop Wily—complete with a somber take on the Megaman 3 title theme.
Continue, which describes how despite all of his talk about wanting to just do it one last time, Mega Man will always keep fighting and always knew that the war will never really end.
One verse in Gamma Unchained has Wily describe what happened with Protoman.
I thought that I could bring the dead back/Broken shell, rusted red with age/I gave him power, a new heart/It filled too quickly with his rage.
In addition, Wily regretting the dark path things have taken, but finding himself unable to give up. The war has gone on so long, and so much has been lost, that he has to make the end justify the means. And so he unleashes Gamma.
Forgive me for what I have done/I've never felt the need to confess/This war has gone on much longer/than any of us would have guessed./I've heard the names that they call me/some sting, some can't help but ring true/I have to live with what I've done/Find the strength to continue
Tell me why I'm the one that they fear/And for him they cheer.
It seems like Air Man's entire reason for being evil is because his power causes him to continually push everyone else away, forcing him to live a bleakly lonely existence. He seals it with the line "If I can't walk among them, then I will walk the world alone." If someone could just give him a hug...
Do you know what it's like to be built this way? With only the power to push others away?
Fly On a Dog, with Megaman lamenting that even with Rush at his side, he feels utterly alone and betrayed by his father.
How dare he call me son? I'm clearly a weapon, a loaded gun.
In I Want To Be The One To Watch You Die, Dr. Light has decided to end the war with Wily once and for all, but the fact that he has to order Mega Man to do it really hurts him.
Son. For one who wants so much to be human, I fear you only see the worst of us. How many more lives must end before he meets his? Put a stop to this. End him. They will forgive you... but I wonder... Am I right to ask this of you?
Dr. Wily's entire personality - the way he knows that people call him a villain, but he legitimately doesn't understand why.
Gamma Unchained: Tell me why I'm the one they fear, when for him they cheer?
Look What You've Done: I only ask that you see what I see. This is the answer, why won't you believe?
Also in Look What You've Done, where Wily seems to imply that he doesn't want Light to be hurt or even vilified: he simply wants his old friend to realize that Wily's ideals were right.
Look What You've Done: I hope history is kind to us all/I know they'll blame me for the fall/I wish there was a better way out/But there's no better way out.
Wily's desperation eventually causes events to spiral entirely out of his control. By the end of History Repeating: Blue, it's not clear that he has any control over either Gamma (What good is power when you're out of control?) or Proto Man (I gave him power, a new heart / It filled too quickly with his rage). Combine that with his belief that he's actually the hero, and his frustration with the fact that he's been unable to convince literally anyone else of that fact, and it's hard not to feel a little bit sorry for the guy, even if everything is ultimately his fault.
Flash Man's last words in "Blue Like You" are pretty heartbreaking:
This moment will last forever/One last moment together!
Needle Man. He's forced to be locked away far underground so that he doesn't harm anybody, and wants to take back all the damage he's accidentally caused. He's so lonely and miserable that part of the reason he's happy about Mega Man coming to fight him is it means that for a short while he won't be alone.
Afraid of the Dark is about Shadow Man consciously losing his former personality to darkness after Dr. Wily repairs and reprograms him—and he's terrified.
The me that used to be here/Has gone away, but I can't say where/I fear I may have killed him/I'm so scared
GeminiEye ends with both personalities realizing they'll never see the sunrise again. Ouch.