See also E25 Notions of de Rham cohomology, for related things.
See also D40 (about Bloch-Ogus theories)
Hermitian-holomorphic Deligne cohomology
Smooth Deligne cohomology, Equivariant smooth Deligne cohomology
Cristalline Deligne cohomology
Deligne cohomology, Deligne-Beilinson cohomology
nLab page on E80 Deligne cohomology and related theories