Eventually, search the database for spectral sequence.
Weight spectral sequence
Descent spectral sequence
Spectral sequences from the six functors formalism
Curtis spectral sequence (mentioned in Toen)
Adams spectral sequence
Grothendieck’s spectral sequence
Leray spectral sequence
Hypercohomology spectral sequence (two, I think)
Motivic spectral sequence
Atiyah-Hirzebruch spectral sequence
Homotopy spectral sequence for a cosimplicial space. Obtained by Bousfield and Kan as a consequence of a model structure on cosimplicial simplicial sets.
Bousfield-Kan spectral sequence: “The prototype of all second-quadrant homotopy spectral sequences”.
Descent spectral sequence. (In Jardine: Gen etale cohomology, p 251, this spectral sequence is for the homotopy groups of a spectrum (or perhaps sheaf of spectra?????). A principle: Bounds on cohomological dimension (in terms of Krull dimension?) force descent spectal sequences to converge.
nLab page on List of spectral sequences