Summing one- and two-dimensional series related to the Euler series

We present results for some infinite series appearing in Feynman diagram calculations, many of which are similar to the Euler series. These include both one-dimensional and two-dimensional series. Most of these series can be expressed in terms of zeta(2), zeta(3), the Catalan constant G and Cl{2}(pi/3) where Cl{2}(theta) is Clausen's function.