Study of the refraction and rightness effects in 2D Archimedean lattice photonic crystals is presented. A special emphasis is placed on possibilities of negative refraction and left-handedness in these structures. Besides the familiar Archimedean lattices like square, triangular, honeycomb and Kagome ones, we consider also, the less known 3 2 4,3,4 (ladybug) and 3,4,6,4 (honeycombring) structures. This involves the calculations of band structures, band-gap maps, equifrequency contours, FDTD simulations of electromagnetic propagation through the structures, as well as an experimental verification of negative refraction at microwaves.