Oftentimes, a specific scene near or at the beginning of a story is what inspires us to write in the first place, or to keep writing. They catalyzed what became the plot, but somewhere in all the revisions, the beginning stopped being relevant. But it's hard to see they need to be cut--how could the scene that sparked the whole idea no longer be relevant?
2. Favorite characters.
Certain characters (usually supporting role) have really cool plotlines or motivations or sub-plotlines that drove some aspect of the story once upon a time. But sometimes they stop being so useful after we've changed how the story goes, which changes how they fit into the story. Then instead of eliminating the character, we find ourselves twisting their background and their presence in the story to MAKE it fit (like the geocentric model of the universe, when nobody wanted to switch over to the heliocentric model).
3. Complicated world issues.
Sometimes adding a plot point that really needs to be added will complicate something in the world that we've never thought about before. To avoid having to change large portions of the world we've spent so much time building, we try to get around adding that plot point (or comparable detail) so we don't have to rethink the world.
4. Personality details
When you cut something from a character's past or present, or change a significant detail about a character's background, the character will change. We get very attached to the people walking around in our heads, telling us these stories. But if something changes, if that defining thing in a character's life no longer exists, or if a situation is completely different from how it was when originally written, the character's actions and reactions WILL change. It's frustrating to rewrite dialogue, especially dialogue we thought was really awesome in some way. It's even worse to have to rethink a character's motivations--sometimes doing that can change the entire plot. But it's necessary, or we make excuses for why a character is acting in a way that has since become out of character. They need room to evolve, just like real humans do.
5. Social commentary
It's easy to insist on keeping a plot a certain way because it makes a point about society or politics or human rights or what have you. But the best social commentaries aren't forced, and if we try to keep in things that aren't working simply for the sake of proving that a classist society is a bad idea (something I often do, as an example) we lose both the potential for a truly compelling plot AND the elegance of writing that needs to accompany a social commentary. We risk our readers feeling as though they're being beaten over the head with commentary, because they can tell we were manipulating the plot in unnatural ways to make a point.
Cutting these darlings can be really difficult (at least, it is for me) because they aren't just scenes that no longer further the plot, or bits of dialogue that don't make sense, or chapters that are bogged down with description and need to be changed. They have the potential to screw up the plot arc of an entire manuscript, and cutting them can also cause you to lose something you really valued about the manuscript itself, whether that be a certain kind of character, a writing move you're proud of, a relationship, or a statement about politics or the world. In essence, a decision to murder one of THESE darlings is a scary thing to make.
But I've noticed that they're like black mold infestations: if you don't catch and take care of them early, you could end up having to remove an entire wall of your house to get rid of them (which actually happened to my dad on a rental property once).
My advice is this: do the thing you're afraid to do. Save an old version of the manuscript (which you ought to do anyway) and just try it. Maybe try it via outline, or just with one segment or chapter or scene. I won't tell you not to be afraid, because that's impossible. But if the only reason you're keeping something is because you're afraid of what will happen to the manuscript if you lose it, have courage, and have faith in yourself. And get out the chainsaw.