http://mathoverflow.net/questions/77071/generalized-beilinson-spectral-sequences
http://mathoverflow.net/questions/100591/galois-acting-on-l-adic-cohomology
http://mathoverflow.net/questions/32248/extraordinary-cohomology-as-a-derived-functor
http://mathoverflow.net/questions/74320/multiplicativity-in-the-descent-spectral-sequence
Goerss-Jardine IV.5. It is defined for any map of simplicial sets, and converges to the homology of . If is a fibration we recover the Serre spectral sequence.
From Goerss-Jardine ch VII: One of the most commonly used tools in homotopy theory is the homotopy spectral sequence of a cosimplicial space. This first appeared in the work of Bousfield and Kan [14] and has been further analyzed by Bousfield [10]. Two of the standard examples include the Bousfield-Kan spectral sequence — an unstable Adams spectral sequence that arose before the general example [7] — and the spectral sequence for computing the homotopy groups of the homotopy inverse limit of a diagram of pointed spaces. One of the main purposes of this chapter is to define and discuss this kind of spectral sequence. We will do much more however; for example, we will give a detailed analysis of the total tower of a cosimplicial space, which is the basic object from which the spectral sequence is derived.
nLab page on Spectral sequence examples