What are the most useful fibrations that one be familiar with in order to use spectral sequences effectively in algebraic topology? There's at least the four different Hopf fibrations and $S^1\to S^{2n+1}\to \mathbb{C}\textrm{P}^n$. Anything else that's useful?
I might add that one fibration I would like someone to explain is the homotopy fiber of a map. I have trouble wrapping my head around it.