Classifying bacteria on the basis of their morphology is extremely difficult; bacteria are generally quite small and have simple shapes, though there are some bacteria, notably the cyanobacteria and actinomycetes, with sufficiently complex morphology to permit classification by shape. In addition to shape, bacteria have traditionally been identified and classified on the basis of their biochemistry and the conditions under which they grow. The advent of molecular biology has made it possible to classify bacteria on the basis of similarities among DNA sequences, and has revolutionized thinking in bacterial systematics. The cladogram above is based on DNA sequences that encode ribosome structure.
For more information on how bacteria are classified, try the eubacterial pages of the Tree of Life.