  We present in an unified and detailed way the nested Bethe ansatz for open
spin chains based on Y(gl(\fn)), Y(gl(\fm|\fn)), U_{q}(gl(\fn)) or
U_{q}(gl(\fm|\fn)) (super)algebras, with arbitrary representations (i.e.
`spins') on each site of the chain and diagonal boundary matrices
(K^+(u),K^-(u)). The nested Bethe anstaz applies for a general K^-(u), but a
particular form of the K^+(u) matrix.
  The construction extends and unifies the results already obtained for open
spin chains based on fundamental representation and for some particular
super-spin chains. We give the eigenvalues, Bethe equations and the form of the
Bethe vectors for the corresponding models. The Bethe vectors are expressed
using a trace formula.
