Most galaxies are either spiral or elliptical (“lenticular” galaxies fall somewhere inbetween).

A typical spiral galaxy, the Pinwheel Galaxy (M101, NGC 5457).

A dwarf elliptical galaxy, M110 (NGC 205).

A new arXiv preprint describes the discovery of LEDA 074886, which has a unique rectangular shape.

LEDA 074886 is thought to have formed as a result of a collision between two disc-shaped elliptical galxies that met “face-on”. The galaxy, 21 megaparsecs (68 million lightyears) away from Earth, is described by the authors of the paper as being “Emerald Cut”, which I think it pretty accurate.

Source: Alister W. Graham et al, “LEDA 074886: A remarkable rectangular-looking galaxy”, arXiv:1203.3608v1.