  Euler sums (also called Zagier sums) occur within the context of knot theory
and quantum field theory. There are various conjectures related to these sums
whose incompletion is a sign that both the mathematics and physics communities
do not yet completely understand the field. Here, we assemble results for
Euler/Zagier sums (also known as multidimensional zeta/harmonic sums) of
arbitrary depth, including sign alternations. Many of our results were obtained
empirically and are apparently new. By carefully compiling and examining a huge
data base of high precision numerical evaluations, we can claim with some
confidence that certain classes of results are exhaustive. While many proofs
are lacking, we have sketched derivations of all results that have so far been
proved.
